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diff --git a/docs/posts/2023-04-30-n-body-simulation.html b/docs/posts/2023-04-30-n-body-simulation.html index cb0bf6c..e12380a 100644 --- a/docs/posts/2023-04-30-n-body-simulation.html +++ b/docs/posts/2023-04-30-n-body-simulation.html @@ -89,46 +89,46 @@ <pre><span></span><code><span class="cm">/*</span> <span class="cm"> * Earth - Sun Orbit Plot</span> <span class="cm"> * Taken from Numerics tutorial</span> -<span class="cm"> */</span><span class="w"></span> - -<span class="kd">const</span><span class="w"> </span><span class="nx">G</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">6.67e-11</span><span class="p">;</span><span class="w"></span> -<span class="kd">const</span><span class="w"> </span><span class="nx">Msun</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">2e30</span><span class="p">;</span><span class="w"></span> -<span class="kd">const</span><span class="w"> </span><span class="nx">AU</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1.5e11</span><span class="p">;</span><span class="w"></span> -<span class="kd">const</span><span class="w"> </span><span class="nx">v0</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">sqrt</span><span class="p">(</span><span class="nx">G</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">Msun</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="nx">AU</span><span class="p">);</span><span class="w"> </span><span class="c1">// SI</span><span class="w"></span> - -<span class="kd">function</span><span class="w"> </span><span class="nx">dR</span><span class="p">(</span><span class="nx">r</span><span class="p">,</span><span class="w"> </span><span class="nx">v</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"></span> -<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">dv</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="o">-</span><span class="nx">G</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">Msun</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">pow</span><span class="p">(</span><span class="nx">r</span><span class="p">[</span><span class="mf">0</span><span class="p">]</span><span class="w"> </span><span class="o">**</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">r</span><span class="p">[</span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">**</span><span class="w"> </span><span class="mf">2</span><span class="p">,</span><span class="w"> </span><span class="mf">3</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">r</span><span class="p">[</span><span class="mf">0</span><span class="p">],</span><span class="w"> </span><span class="o">-</span><span class="nx">G</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">Msun</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">pow</span><span class="p">(</span><span class="nx">r</span><span class="p">[</span><span class="mf">0</span><span class="p">]</span><span class="w"> </span><span class="o">**</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">r</span><span class="p">[</span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">**</span><span class="w"> </span><span class="mf">2</span><span class="p">,</span><span class="w"> </span><span class="mf">3</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">r</span><span class="p">[</span><span class="mf">1</span><span class="p">]];</span><span class="w"></span> -<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">dr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[...</span><span class="nx">v</span><span class="p">];</span><span class="w"></span> -<span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="p">[</span><span class="nx">dr</span><span class="p">,</span><span class="w"> </span><span class="nx">dv</span><span class="p">];</span><span class="w"></span> -<span class="p">}</span><span class="w"></span> - -<span class="c1">// initialize system</span><span class="w"></span> -<span class="kd">let</span><span class="w"> </span><span class="nx">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="o">-</span><span class="nx">AU</span><span class="p">,</span><span class="w"> </span><span class="mf">0</span><span class="p">];</span><span class="w"></span> -<span class="kd">const</span><span class="w"> </span><span class="nx">theta</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">atan2</span><span class="p">(</span><span class="nx">r</span><span class="p">[</span><span class="mf">1</span><span class="p">],</span><span class="w"> </span><span class="nx">r</span><span class="p">[</span><span class="mf">0</span><span class="p">]);</span><span class="w"></span> -<span class="kd">let</span><span class="w"> </span><span class="nx">v</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="o">-</span><span class="nx">v0</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">sin</span><span class="p">(</span><span class="nx">theta</span><span class="p">),</span><span class="w"> </span><span class="nx">v0</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">cos</span><span class="p">(</span><span class="nx">theta</span><span class="p">)];</span><span class="w"></span> - -<span class="kd">const</span><span class="w"> </span><span class="nx">t</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">.</span><span class="kr">from</span><span class="p">({</span><span class="w"> </span><span class="nx">length</span><span class="o">:</span><span class="w"> </span><span class="mf">1001</span><span class="w"> </span><span class="p">},</span><span class="w"> </span><span class="p">(</span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">100</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">0.0</span><span class="p">);</span><span class="w"> </span><span class="c1">// years</span><span class="w"></span> -<span class="kd">const</span><span class="w"> </span><span class="nx">yearSec</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">365</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mf">24</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mf">3600</span><span class="p">;</span><span class="w"></span> -<span class="kd">const</span><span class="w"> </span><span class="nx">dt</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="nx">t</span><span class="p">[</span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">t</span><span class="p">[</span><span class="mf">0</span><span class="p">])</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">yearSec</span><span class="p">;</span><span class="w"> </span><span class="c1">// s</span><span class="w"></span> -<span class="kd">const</span><span class="w"> </span><span class="nx">x4Plot</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">.</span><span class="kr">from</span><span class="p">({</span><span class="w"> </span><span class="nx">length</span><span class="o">:</span><span class="w"> </span><span class="nx">t</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="p">},</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="mf">0</span><span class="p">);</span><span class="w"></span> -<span class="kd">const</span><span class="w"> </span><span class="nx">y4Plot</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">.</span><span class="kr">from</span><span class="p">({</span><span class="w"> </span><span class="nx">length</span><span class="o">:</span><span class="w"> </span><span class="nx">t</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="p">},</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="mf">0</span><span class="p">);</span><span class="w"></span> - -<span class="c1">// integrate using RK4!</span><span class="w"></span> -<span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">t</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"></span> -<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">k1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dR</span><span class="p">(</span><span class="nx">r</span><span class="p">,</span><span class="w"> </span><span class="nx">v</span><span class="p">).</span><span class="nx">map</span><span class="p">(</span><span class="nx">x</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="nx">x</span><span class="p">.</span><span class="nx">map</span><span class="p">(</span><span class="nx">y</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="nx">y</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">dt</span><span class="p">));</span><span class="w"></span> -<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">k2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dR</span><span class="p">(</span><span class="nx">r</span><span class="p">.</span><span class="nx">map</span><span class="p">((</span><span class="nx">ri</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="p">)</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="nx">ri</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">k1</span><span class="p">[</span><span class="mf">0</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">),</span><span class="w"> </span><span class="nx">v</span><span class="p">.</span><span class="nx">map</span><span class="p">((</span><span class="nx">vi</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="p">)</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="nx">vi</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">k1</span><span class="p">[</span><span class="mf">1</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">)).</span><span class="nx">map</span><span class="p">(</span><span class="nx">x</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="nx">x</span><span class="p">.</span><span class="nx">map</span><span class="p">(</span><span class="nx">y</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="nx">y</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">dt</span><span class="p">));</span><span class="w"></span> -<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">k3</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dR</span><span class="p">(</span><span class="nx">r</span><span class="p">.</span><span class="nx">map</span><span class="p">((</span><span class="nx">ri</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="p">)</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="nx">ri</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">k2</span><span class="p">[</span><span class="mf">0</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">),</span><span class="w"> </span><span class="nx">v</span><span class="p">.</span><span class="nx">map</span><span class="p">((</span><span class="nx">vi</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="p">)</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="nx">vi</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">k2</span><span class="p">[</span><span class="mf">1</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">)).</span><span class="nx">map</span><span class="p">(</span><span class="nx">x</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="nx">x</span><span class="p">.</span><span class="nx">map</span><span class="p">(</span><span class="nx">y</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="nx">y</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">dt</span><span class="p">));</span><span class="w"></span> -<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">k4</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dR</span><span class="p">(</span><span class="nx">r</span><span class="p">.</span><span class="nx">map</span><span class="p">((</span><span class="nx">ri</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="p">)</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="nx">ri</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">k3</span><span class="p">[</span><span class="mf">0</span><span class="p">][</span><span class="nx">j</span><span class="p">]),</span><span class="w"> </span><span class="nx">v</span><span class="p">.</span><span class="nx">map</span><span class="p">((</span><span class="nx">vi</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="p">)</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="nx">vi</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">k3</span><span class="p">[</span><span class="mf">1</span><span class="p">][</span><span class="nx">j</span><span class="p">])).</span><span class="nx">map</span><span class="p">(</span><span class="nx">x</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="nx">x</span><span class="p">.</span><span class="nx">map</span><span class="p">(</span><span class="nx">y</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="nx">y</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">dt</span><span class="p">));</span><span class="w"></span> -<span class="w"> </span><span class="nx">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">r</span><span class="p">.</span><span class="nx">map</span><span class="p">((</span><span class="nx">ri</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="p">)</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="nx">ri</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="nx">k1</span><span class="p">[</span><span class="mf">0</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">k2</span><span class="p">[</span><span class="mf">0</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">k3</span><span class="p">[</span><span class="mf">0</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">k4</span><span class="p">[</span><span class="mf">0</span><span class="p">][</span><span class="nx">j</span><span class="p">])</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">6</span><span class="p">);</span><span class="w"></span> -<span class="w"> </span><span class="nx">v</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">v</span><span class="p">.</span><span class="nx">map</span><span class="p">((</span><span class="nx">vi</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="p">)</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="nx">vi</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="nx">k1</span><span class="p">[</span><span class="mf">1</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">k2</span><span class="p">[</span><span class="mf">1</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">k3</span><span class="p">[</span><span class="mf">1</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">k4</span><span class="p">[</span><span class="mf">1</span><span class="p">][</span><span class="nx">j</span><span class="p">])</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">6</span><span class="p">);</span><span class="w"></span> -<span class="w"> </span><span class="nx">x4Plot</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">r</span><span class="p">[</span><span class="mf">0</span><span class="p">];</span><span class="w"></span> -<span class="w"> </span><span class="nx">y4Plot</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">r</span><span class="p">[</span><span class="mf">1</span><span class="p">];</span><span class="w"></span> -<span class="p">}</span><span class="w"></span> - -<span class="c1">// make data for plot</span><span class="w"></span> -<span class="kd">var</span><span class="w"> </span><span class="nx">sun</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nx">x</span><span class="o">:</span><span class="w"> </span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="nx">y</span><span class="o">:</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="p">};</span><span class="w"></span> -<span class="kd">const</span><span class="w"> </span><span class="nx">earth</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nx">x</span><span class="o">:</span><span class="w"> </span><span class="nx">x4Plot</span><span class="p">.</span><span class="nx">map</span><span class="p">(</span><span class="nx">x</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="nx">x</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="nx">AU</span><span class="p">),</span><span class="w"> </span><span class="nx">y</span><span class="o">:</span><span class="w"> </span><span class="nx">y4Plot</span><span class="p">.</span><span class="nx">map</span><span class="p">(</span><span class="nx">y</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="nx">y</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="nx">AU</span><span class="p">)</span><span class="w"> </span><span class="p">};</span><span class="w"></span> -<span class="kd">const</span><span class="w"> </span><span class="nx">circle</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nx">x</span><span class="o">:</span><span class="w"> </span><span class="nb">Array</span><span class="p">.</span><span class="kr">from</span><span class="p">({</span><span class="w"> </span><span class="nx">length</span><span class="o">:</span><span class="w"> </span><span class="mf">1001</span><span class="w"> </span><span class="p">},</span><span class="w"> </span><span class="p">(</span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">cos</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">100</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">PI</span><span class="p">)),</span><span class="w"> </span><span class="nx">y</span><span class="o">:</span><span class="w"> </span><span class="nb">Array</span><span class="p">.</span><span class="kr">from</span><span class="p">({</span><span class="w"> </span><span class="nx">length</span><span class="o">:</span><span class="w"> </span><span class="mf">1001</span><span class="w"> </span><span class="p">},</span><span class="w"> </span><span class="p">(</span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">sin</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">100</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">PI</span><span class="p">))</span><span class="w"> </span><span class="p">};</span><span class="w"></span> +<span class="cm"> */</span> + +<span class="kd">const</span><span class="w"> </span><span class="nx">G</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">6.67e-11</span><span class="p">;</span> +<span class="kd">const</span><span class="w"> </span><span class="nx">Msun</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">2e30</span><span class="p">;</span> +<span class="kd">const</span><span class="w"> </span><span class="nx">AU</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1.5e11</span><span class="p">;</span> +<span class="kd">const</span><span class="w"> </span><span class="nx">v0</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">sqrt</span><span class="p">(</span><span class="nx">G</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">Msun</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="nx">AU</span><span class="p">);</span><span class="w"> </span><span class="c1">// SI</span> + +<span class="kd">function</span><span class="w"> </span><span class="nx">dR</span><span class="p">(</span><span class="nx">r</span><span class="p">,</span><span class="w"> </span><span class="nx">v</span><span class="p">)</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">dv</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="o">-</span><span class="nx">G</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">Msun</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">pow</span><span class="p">(</span><span class="nx">r</span><span class="p">[</span><span class="mf">0</span><span class="p">]</span><span class="w"> </span><span class="o">**</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">r</span><span class="p">[</span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">**</span><span class="w"> </span><span class="mf">2</span><span class="p">,</span><span class="w"> </span><span class="mf">3</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">r</span><span class="p">[</span><span class="mf">0</span><span class="p">],</span><span class="w"> </span><span class="o">-</span><span class="nx">G</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">Msun</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">pow</span><span class="p">(</span><span class="nx">r</span><span class="p">[</span><span class="mf">0</span><span class="p">]</span><span class="w"> </span><span class="o">**</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">r</span><span class="p">[</span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">**</span><span class="w"> </span><span class="mf">2</span><span class="p">,</span><span class="w"> </span><span class="mf">3</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">r</span><span class="p">[</span><span class="mf">1</span><span class="p">]];</span> +<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">dr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[...</span><span class="nx">v</span><span class="p">];</span> +<span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="p">[</span><span class="nx">dr</span><span class="p">,</span><span class="w"> </span><span class="nx">dv</span><span class="p">];</span> +<span class="p">}</span> + +<span class="c1">// initialize system</span> +<span class="kd">let</span><span class="w"> </span><span class="nx">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="o">-</span><span class="nx">AU</span><span class="p">,</span><span class="w"> </span><span class="mf">0</span><span class="p">];</span> +<span class="kd">const</span><span class="w"> </span><span class="nx">theta</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">atan2</span><span class="p">(</span><span class="nx">r</span><span class="p">[</span><span class="mf">1</span><span class="p">],</span><span class="w"> </span><span class="nx">r</span><span class="p">[</span><span class="mf">0</span><span class="p">]);</span> +<span class="kd">let</span><span class="w"> </span><span class="nx">v</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="o">-</span><span class="nx">v0</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">sin</span><span class="p">(</span><span class="nx">theta</span><span class="p">),</span><span class="w"> </span><span class="nx">v0</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">cos</span><span class="p">(</span><span class="nx">theta</span><span class="p">)];</span> + +<span class="kd">const</span><span class="w"> </span><span class="nx">t</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">.</span><span class="kr">from</span><span class="p">({</span><span class="w"> </span><span class="nx">length</span><span class="o">:</span><span class="w"> </span><span class="mf">1001</span><span class="w"> </span><span class="p">},</span><span class="w"> </span><span class="p">(</span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">100</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">0.0</span><span class="p">);</span><span class="w"> </span><span class="c1">// years</span> +<span class="kd">const</span><span class="w"> </span><span class="nx">yearSec</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">365</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mf">24</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mf">3600</span><span class="p">;</span> +<span class="kd">const</span><span class="w"> </span><span class="nx">dt</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="nx">t</span><span class="p">[</span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">t</span><span class="p">[</span><span class="mf">0</span><span class="p">])</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">yearSec</span><span class="p">;</span><span class="w"> </span><span class="c1">// s</span> +<span class="kd">const</span><span class="w"> </span><span class="nx">x4Plot</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">.</span><span class="kr">from</span><span class="p">({</span><span class="w"> </span><span class="nx">length</span><span class="o">:</span><span class="w"> </span><span class="nx">t</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="p">},</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="mf">0</span><span class="p">);</span> +<span class="kd">const</span><span class="w"> </span><span class="nx">y4Plot</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">.</span><span class="kr">from</span><span class="p">({</span><span class="w"> </span><span class="nx">length</span><span class="o">:</span><span class="w"> </span><span class="nx">t</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="p">},</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="mf">0</span><span class="p">);</span> + +<span class="c1">// integrate using RK4!</span> +<span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">t</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">k1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dR</span><span class="p">(</span><span class="nx">r</span><span class="p">,</span><span class="w"> </span><span class="nx">v</span><span class="p">).</span><span class="nx">map</span><span class="p">(</span><span class="nx">x</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="nx">x</span><span class="p">.</span><span class="nx">map</span><span class="p">(</span><span class="nx">y</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="nx">y</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">dt</span><span class="p">));</span> +<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">k2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dR</span><span class="p">(</span><span class="nx">r</span><span class="p">.</span><span class="nx">map</span><span class="p">((</span><span class="nx">ri</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="p">)</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="nx">ri</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">k1</span><span class="p">[</span><span class="mf">0</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">),</span><span class="w"> </span><span class="nx">v</span><span class="p">.</span><span class="nx">map</span><span class="p">((</span><span class="nx">vi</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="p">)</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="nx">vi</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">k1</span><span class="p">[</span><span class="mf">1</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">)).</span><span class="nx">map</span><span class="p">(</span><span class="nx">x</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="nx">x</span><span class="p">.</span><span class="nx">map</span><span class="p">(</span><span class="nx">y</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="nx">y</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">dt</span><span class="p">));</span> +<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">k3</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dR</span><span class="p">(</span><span class="nx">r</span><span class="p">.</span><span class="nx">map</span><span class="p">((</span><span class="nx">ri</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="p">)</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="nx">ri</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">k2</span><span class="p">[</span><span class="mf">0</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">),</span><span class="w"> </span><span class="nx">v</span><span class="p">.</span><span class="nx">map</span><span class="p">((</span><span class="nx">vi</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="p">)</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="nx">vi</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">k2</span><span class="p">[</span><span class="mf">1</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">)).</span><span class="nx">map</span><span class="p">(</span><span class="nx">x</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="nx">x</span><span class="p">.</span><span class="nx">map</span><span class="p">(</span><span class="nx">y</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="nx">y</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">dt</span><span class="p">));</span> +<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">k4</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dR</span><span class="p">(</span><span class="nx">r</span><span class="p">.</span><span class="nx">map</span><span class="p">((</span><span class="nx">ri</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="p">)</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="nx">ri</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">k3</span><span class="p">[</span><span class="mf">0</span><span class="p">][</span><span class="nx">j</span><span class="p">]),</span><span class="w"> </span><span class="nx">v</span><span class="p">.</span><span class="nx">map</span><span class="p">((</span><span class="nx">vi</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="p">)</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="nx">vi</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">k3</span><span class="p">[</span><span class="mf">1</span><span class="p">][</span><span class="nx">j</span><span class="p">])).</span><span class="nx">map</span><span class="p">(</span><span class="nx">x</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="nx">x</span><span class="p">.</span><span class="nx">map</span><span class="p">(</span><span class="nx">y</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="nx">y</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">dt</span><span class="p">));</span> +<span class="w"> </span><span class="nx">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">r</span><span class="p">.</span><span class="nx">map</span><span class="p">((</span><span class="nx">ri</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="p">)</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="nx">ri</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="nx">k1</span><span class="p">[</span><span class="mf">0</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">k2</span><span class="p">[</span><span class="mf">0</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">k3</span><span class="p">[</span><span class="mf">0</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">k4</span><span class="p">[</span><span class="mf">0</span><span class="p">][</span><span class="nx">j</span><span class="p">])</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">6</span><span class="p">);</span> +<span class="w"> </span><span class="nx">v</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">v</span><span class="p">.</span><span class="nx">map</span><span class="p">((</span><span class="nx">vi</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="p">)</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="nx">vi</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="nx">k1</span><span class="p">[</span><span class="mf">1</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">k2</span><span class="p">[</span><span class="mf">1</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">k3</span><span class="p">[</span><span class="mf">1</span><span class="p">][</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">k4</span><span class="p">[</span><span class="mf">1</span><span class="p">][</span><span class="nx">j</span><span class="p">])</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">6</span><span class="p">);</span> +<span class="w"> </span><span class="nx">x4Plot</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">r</span><span class="p">[</span><span class="mf">0</span><span class="p">];</span> +<span class="w"> </span><span class="nx">y4Plot</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">r</span><span class="p">[</span><span class="mf">1</span><span class="p">];</span> +<span class="p">}</span> + +<span class="c1">// make data for plot</span> +<span class="kd">var</span><span class="w"> </span><span class="nx">sun</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nx">x</span><span class="o">:</span><span class="w"> </span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="nx">y</span><span class="o">:</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="p">};</span> +<span class="kd">const</span><span class="w"> </span><span class="nx">earth</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nx">x</span><span class="o">:</span><span class="w"> </span><span class="nx">x4Plot</span><span class="p">.</span><span class="nx">map</span><span class="p">(</span><span class="nx">x</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="nx">x</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="nx">AU</span><span class="p">),</span><span class="w"> </span><span class="nx">y</span><span class="o">:</span><span class="w"> </span><span class="nx">y4Plot</span><span class="p">.</span><span class="nx">map</span><span class="p">(</span><span class="nx">y</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="nx">y</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="nx">AU</span><span class="p">)</span><span class="w"> </span><span class="p">};</span> +<span class="kd">const</span><span class="w"> </span><span class="nx">circle</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nx">x</span><span class="o">:</span><span class="w"> </span><span class="nb">Array</span><span class="p">.</span><span class="kr">from</span><span class="p">({</span><span class="w"> </span><span class="nx">length</span><span class="o">:</span><span class="w"> </span><span class="mf">1001</span><span class="w"> </span><span class="p">},</span><span class="w"> </span><span class="p">(</span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">cos</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">100</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">PI</span><span class="p">)),</span><span class="w"> </span><span class="nx">y</span><span class="o">:</span><span class="w"> </span><span class="nb">Array</span><span class="p">.</span><span class="kr">from</span><span class="p">({</span><span class="w"> </span><span class="nx">length</span><span class="o">:</span><span class="w"> </span><span class="mf">1001</span><span class="w"> </span><span class="p">},</span><span class="w"> </span><span class="p">(</span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">sin</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">100</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">PI</span><span class="p">))</span><span class="w"> </span><span class="p">};</span> </code></pre> </div> @@ -150,76 +150,77 @@ Next, the function dR takes the position r and velocity v of Earth as input and <h3>Plotting the orbit</h3> -<p>Now that we have the data for the Sun's position, Earth's orbit, and the reference circle, we can plot them using Plotly.js. - <div class="codehilite"> - <pre><span></span><code><span class="kd">let</span><span class="w"> </span><span class="nx">traceSun</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="w"></span> - <span class="w"> </span><span class="nx">x</span><span class="o">:</span><span class="w"> </span><span class="p">[</span><span class="nx">sun</span><span class="p">.</span><span class="nx">x</span><span class="p">],</span><span class="w"></span> - <span class="w"> </span><span class="nx">y</span><span class="o">:</span><span class="w"> </span><span class="p">[</span><span class="nx">sun</span><span class="p">.</span><span class="nx">y</span><span class="p">],</span><span class="w"></span> - <span class="w"> </span><span class="nx">mode</span><span class="o">:</span><span class="w"> </span><span class="s2">"markers"</span><span class="p">,</span><span class="w"></span> - <span class="w"> </span><span class="nx">marker</span><span class="o">:</span><span class="w"> </span><span class="p">{</span><span class="w"></span> - <span class="w"> </span><span class="nx">symbol</span><span class="o">:</span><span class="w"> </span><span class="s2">"star"</span><span class="p">,</span><span class="w"></span> - <span class="w"> </span><span class="nx">size</span><span class="o">:</span><span class="w"> </span><span class="mf">10</span><span class="p">,</span><span class="w"></span> - <span class="w"> </span><span class="nx">color</span><span class="o">:</span><span class="w"> </span><span class="s2">"gold"</span><span class="p">,</span><span class="w"></span> - <span class="w"> </span><span class="p">},</span><span class="w"></span> - <span class="w"> </span><span class="nx">name</span><span class="o">:</span><span class="w"> </span><span class="s2">"Sun"</span><span class="p">,</span><span class="w"></span> - <span class="p">};</span><span class="w"></span> - <br /> - <span class="kd">const</span><span class="w"> </span><span class="nx">traceEarth</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="w"></span> - <span class="w"> </span><span class="nx">x</span><span class="o">:</span><span class="w"> </span><span class="nx">earth</span><span class="p">.</span><span class="nx">x</span><span class="p">,</span><span class="w"></span> - <span class="w"> </span><span class="nx">y</span><span class="o">:</span><span class="w"> </span><span class="nx">earth</span><span class="p">.</span><span class="nx">y</span><span class="p">,</span><span class="w"></span> - <span class="w"> </span><span class="nx">mode</span><span class="o">:</span><span class="w"> </span><span class="s2">"lines"</span><span class="p">,</span><span class="w"></span> - <span class="w"> </span><span class="nx">line</span><span class="o">:</span><span class="w"> </span><span class="p">{</span><span class="w"></span> - <span class="w"> </span><span class="nx">color</span><span class="o">:</span><span class="w"> </span><span class="s2">"white"</span><span class="w"></span> - <span class="w"> </span><span class="p">},</span><span class="w"></span> - <span class="w"> </span><span class="nx">name</span><span class="o">:</span><span class="w"> </span><span class="s2">"Earth"</span><span class="p">,</span><span class="w"></span> - <span class="p">};</span><span class="w"></span> - <br /> - <span class="kd">const</span><span class="w"> </span><span class="nx">traceOrbit</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="w"></span> - <span class="w"> </span><span class="nx">x</span><span class="o">:</span><span class="w"> </span><span class="nx">circle</span><span class="p">.</span><span class="nx">x</span><span class="p">,</span><span class="w"></span> - <span class="w"> </span><span class="nx">y</span><span class="o">:</span><span class="nx">circle</span><span class="p">.</span><span class="nx">y</span><span class="p">,</span><span class="w"></span> - <span class="w"> </span><span class="nx">mode</span><span class="o">:</span><span class="w"> </span><span class="s2">"lines"</span><span class="p">,</span><span class="w"></span> - <span class="w"> </span><span class="nx">line</span><span class="o">:</span><span class="w"> </span><span class="p">{</span><span class="w"></span> - <span class="w"> </span><span class="nx">color</span><span class="o">:</span><span class="w"> </span><span class="s2">"crimson"</span><span class="p">,</span><span class="w"></span> - <span class="w"> </span><span class="nx">dash</span><span class="o">:</span><span class="w"> </span><span class="s2">"dash"</span><span class="w"></span> - <span class="w"> </span><span class="p">},</span><span class="w"></span> - <span class="w"> </span><span class="nx">name</span><span class="o">:</span><span class="w"> </span><span class="s2">"1 AU Circle"</span><span class="p">,</span><span class="w"></span> - <span class="p">};</span><span class="w"></span> - <br /> - <span class="kd">const</span><span class="w"> </span><span class="nx">earthSunLayout</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="w"></span> - <span class="w"> </span><span class="nx">title</span><span class="o">:</span><span class="w"> </span><span class="s2">"Earth-Sun Orbit"</span><span class="p">,</span><span class="w"></span> - <span class="w"> </span><span class="nx">xaxis</span><span class="o">:</span><span class="w"> </span><span class="p">{</span><span class="w"></span> - <span class="w"> </span><span class="nx">title</span><span class="o">:</span><span class="w"> </span><span class="s2">"x [AU]"</span><span class="p">,</span><span class="w"></span> - <span class="w"> </span><span class="nx">range</span><span class="o">:</span><span class="w"> </span><span class="p">[</span><span class="o">-</span><span class="mf">1.1</span><span class="p">,</span><span class="mf">1.1</span><span class="p">],</span><span class="w"></span> - <span class="w"> </span><span class="nx">showgrid</span><span class="o">:</span><span class="w"> </span><span class="kc">true</span><span class="p">,</span><span class="w"></span> - <span class="w"> </span><span class="nx">gridcolor</span><span class="o">:</span><span class="w"> </span><span class="s2">"rgba(255,255,255,0.5)"</span><span class="p">,</span><span class="w"></span> - <span class="w"> </span><span class="nx">gridwidth</span><span class="o">:</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span><span class="w"></span> - <span class="w"> </span><span class="nx">zeroline</span><span class="o">:</span><span class="w"> </span><span class="kc">true</span><span class="p">,</span><span class="w"></span> - <span class="w"> </span><span class="nx">tickmode</span><span class="o">:</span><span class="w"> </span><span class="s2">"auto"</span><span class="p">,</span><span class="w"></span> - <span class="w"> </span><span class="nx">nticks</span><span class="o">:</span><span class="w"> </span><span class="mf">5</span><span class="p">,</span><span class="w"></span> - <span class="w"> </span><span class="p">},</span><span class="w"></span> - <span class="w"> </span><span class="nx">yaxis</span><span class="o">:</span><span class="w"> </span><span class="p">{</span><span class="w"></span> - <span class="w"> </span><span class="nx">title</span><span class="o">:</span><span class="w"> </span><span class="s2">"y [AU]"</span><span class="p">,</span><span class="w"></span> - <span class="w"> </span><span class="nx">range</span><span class="o">:</span><span class="w"> </span><span class="p">[</span><span class="o">-</span><span class="mf">1.1</span><span class="p">,</span><span class="mf">1.1</span><span class="p">],</span><span class="w"></span> - <span class="w"> </span><span class="nx">showgrid</span><span class="o">:</span><span class="w"> </span><span class="kc">true</span><span class="p">,</span><span class="w"></span> - <span class="w"> </span><span class="nx">gridcolor</span><span class="o">:</span><span class="w"> </span><span class="s2">"rgba(255,255,255,0.5)"</span><span class="p">,</span><span class="w"></span> - <span class="w"> </span><span class="nx">gridwidth</span><span class="o">:</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span><span class="w"></span> - <span class="w"> </span><span class="nx">zeroline</span><span class="o">:</span><span class="w"> </span><span class="kc">false</span><span class="p">,</span><span class="w"></span> - <span class="w"> </span><span class="nx">tickmode</span><span class="o">:</span><span class="w"> </span><span class="s2">"auto"</span><span class="p">,</span><span class="w"></span> - <span class="w"> </span><span class="nx">nticks</span><span class="o">:</span><span class="w"> </span><span class="mf">5</span><span class="p">,</span><span class="w"></span> - <span class="w"> </span><span class="p">},</span><span class="w"></span> - <span class="w"> </span><span class="nx">margin</span><span class="o">:</span><span class="w"> </span><span class="p">{</span><span class="w"></span> - <span class="w"> </span><span class="nx">l</span><span class="o">:</span><span class="w"> </span><span class="mf">50</span><span class="p">,</span><span class="w"></span> - <span class="w"> </span><span class="nx">r</span><span class="o">:</span><span class="w"> </span><span class="mf">50</span><span class="p">,</span><span class="w"></span> - <span class="w"> </span><span class="nx">b</span><span class="o">:</span><span class="w"> </span><span class="mf">50</span><span class="p">,</span><span class="w"></span> - <span class="w"> </span><span class="nx">t</span><span class="o">:</span><span class="w"> </span><span class="mf">50</span><span class="p">,</span><span class="w"></span> - <span class="w"> </span><span class="nx">pad</span><span class="o">:</span><span class="w"> </span><span class="mf">4</span><span class="p">,</span><span class="w"></span> - <span class="w"> </span><span class="p">},</span><span class="w"></span> - <span class="w"> </span><span class="nx">paper<em>bgcolor</span><span class="o">:</span><span class="w"> </span><span class="s2">"black"</span><span class="p">,</span><span class="w"></span> - <span class="w"> </span><span class="nx">plot</em>bgcolor</span><span class="o">:</span><span class="w"> </span><span class="s2">"black"</span><span class="p">,</span><span class="w"></span> - <span class="p">};</span><span class="w"></span> - <span class="nx">Plotly</span><span class="p">.</span><span class="nx">newPlot</span><span class="p">(</span><span class="s2">"plot"</span><span class="p">,[</span><span class="nx">traceSun</span><span class="p">,</span><span class="nx">traceEarth</span><span class="p">,</span><span class="nx">traceOrbit</span><span class="p">],</span><span class="w"> </span><span class="nx">earthSunLayout</span><span class="p">);</span><span class="w"></span> - </code></pre> - </div></p> +<p>Now that we have the data for the Sun's position, Earth's orbit, and the reference circle, we can plot them using Plotly.js.</p> + +<div class="codehilite"> +<pre><span></span><code><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">traceSun</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="nx">x</span><span class="o">:</span><span class="w"> </span><span class="p">[</span><span class="nx">sun</span><span class="p">.</span><span class="nx">x</span><span class="p">],</span> +<span class="w"> </span><span class="nx">y</span><span class="o">:</span><span class="w"> </span><span class="p">[</span><span class="nx">sun</span><span class="p">.</span><span class="nx">y</span><span class="p">],</span> +<span class="w"> </span><span class="nx">mode</span><span class="o">:</span><span class="w"> </span><span class="s2">"markers"</span><span class="p">,</span> +<span class="w"> </span><span class="nx">marker</span><span class="o">:</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="nx">symbol</span><span class="o">:</span><span class="w"> </span><span class="s2">"star"</span><span class="p">,</span> +<span class="w"> </span><span class="nx">size</span><span class="o">:</span><span class="w"> </span><span class="mf">10</span><span class="p">,</span> +<span class="w"> </span><span class="nx">color</span><span class="o">:</span><span class="w"> </span><span class="s2">"gold"</span><span class="p">,</span> +<span class="w"> </span><span class="p">},</span> +<span class="w"> </span><span class="nx">name</span><span class="o">:</span><span class="w"> </span><span class="s2">"Sun"</span><span class="p">,</span> +<span class="w"> </span><span class="p">};</span> + +<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">traceEarth</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="nx">x</span><span class="o">:</span><span class="w"> </span><span class="nx">earth</span><span class="p">.</span><span class="nx">x</span><span class="p">,</span> +<span class="w"> </span><span class="nx">y</span><span class="o">:</span><span class="w"> </span><span class="nx">earth</span><span class="p">.</span><span class="nx">y</span><span class="p">,</span> +<span class="w"> </span><span class="nx">mode</span><span class="o">:</span><span class="w"> </span><span class="s2">"lines"</span><span class="p">,</span> +<span class="w"> </span><span class="nx">line</span><span class="o">:</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="nx">color</span><span class="o">:</span><span class="w"> </span><span class="s2">"white"</span> +<span class="w"> </span><span class="p">},</span> +<span class="w"> </span><span class="nx">name</span><span class="o">:</span><span class="w"> </span><span class="s2">"Earth"</span><span class="p">,</span> +<span class="w"> </span><span class="p">};</span> + +<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">traceOrbit</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="nx">x</span><span class="o">:</span><span class="w"> </span><span class="nx">circle</span><span class="p">.</span><span class="nx">x</span><span class="p">,</span> +<span class="w"> </span><span class="nx">y</span><span class="o">:</span><span class="nx">circle</span><span class="p">.</span><span class="nx">y</span><span class="p">,</span> +<span class="w"> </span><span class="nx">mode</span><span class="o">:</span><span class="w"> </span><span class="s2">"lines"</span><span class="p">,</span> +<span class="w"> </span><span class="nx">line</span><span class="o">:</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="nx">color</span><span class="o">:</span><span class="w"> </span><span class="s2">"crimson"</span><span class="p">,</span> +<span class="w"> </span><span class="nx">dash</span><span class="o">:</span><span class="w"> </span><span class="s2">"dash"</span> +<span class="w"> </span><span class="p">},</span> +<span class="w"> </span><span class="nx">name</span><span class="o">:</span><span class="w"> </span><span class="s2">"1 AU Circle"</span><span class="p">,</span> +<span class="w"> </span><span class="p">};</span> + +<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">earthSunLayout</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="nx">title</span><span class="o">:</span><span class="w"> </span><span class="s2">"Earth-Sun Orbit"</span><span class="p">,</span> +<span class="w"> </span><span class="nx">xaxis</span><span class="o">:</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="nx">title</span><span class="o">:</span><span class="w"> </span><span class="s2">"x [AU]"</span><span class="p">,</span> +<span class="w"> </span><span class="nx">range</span><span class="o">:</span><span class="w"> </span><span class="p">[</span><span class="o">-</span><span class="mf">1.1</span><span class="p">,</span><span class="mf">1.1</span><span class="p">],</span> +<span class="w"> </span><span class="nx">showgrid</span><span class="o">:</span><span class="w"> </span><span class="kc">true</span><span class="p">,</span> +<span class="w"> </span><span class="nx">gridcolor</span><span class="o">:</span><span class="w"> </span><span class="s2">"rgba(255,255,255,0.5)"</span><span class="p">,</span> +<span class="w"> </span><span class="nx">gridwidth</span><span class="o">:</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span> +<span class="w"> </span><span class="nx">zeroline</span><span class="o">:</span><span class="w"> </span><span class="kc">true</span><span class="p">,</span> +<span class="w"> </span><span class="nx">tickmode</span><span class="o">:</span><span class="w"> </span><span class="s2">"auto"</span><span class="p">,</span> +<span class="w"> </span><span class="nx">nticks</span><span class="o">:</span><span class="w"> </span><span class="mf">5</span><span class="p">,</span> +<span class="w"> </span><span class="p">},</span> +<span class="w"> </span><span class="nx">yaxis</span><span class="o">:</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="nx">title</span><span class="o">:</span><span class="w"> </span><span class="s2">"y [AU]"</span><span class="p">,</span> +<span class="w"> </span><span class="nx">range</span><span class="o">:</span><span class="w"> </span><span class="p">[</span><span class="o">-</span><span class="mf">1.1</span><span class="p">,</span><span class="mf">1.1</span><span class="p">],</span> +<span class="w"> </span><span class="nx">showgrid</span><span class="o">:</span><span class="w"> </span><span class="kc">true</span><span class="p">,</span> +<span class="w"> </span><span class="nx">gridcolor</span><span class="o">:</span><span class="w"> </span><span class="s2">"rgba(255,255,255,0.5)"</span><span class="p">,</span> +<span class="w"> </span><span class="nx">gridwidth</span><span class="o">:</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span> +<span class="w"> </span><span class="nx">zeroline</span><span class="o">:</span><span class="w"> </span><span class="kc">false</span><span class="p">,</span> +<span class="w"> </span><span class="nx">tickmode</span><span class="o">:</span><span class="w"> </span><span class="s2">"auto"</span><span class="p">,</span> +<span class="w"> </span><span class="nx">nticks</span><span class="o">:</span><span class="w"> </span><span class="mf">5</span><span class="p">,</span> +<span class="w"> </span><span class="p">},</span> +<span class="w"> </span><span class="nx">margin</span><span class="o">:</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="nx">l</span><span class="o">:</span><span class="w"> </span><span class="mf">50</span><span class="p">,</span> +<span class="w"> </span><span class="nx">r</span><span class="o">:</span><span class="w"> </span><span class="mf">50</span><span class="p">,</span> +<span class="w"> </span><span class="nx">b</span><span class="o">:</span><span class="w"> </span><span class="mf">50</span><span class="p">,</span> +<span class="w"> </span><span class="nx">t</span><span class="o">:</span><span class="w"> </span><span class="mf">50</span><span class="p">,</span> +<span class="w"> </span><span class="nx">pad</span><span class="o">:</span><span class="w"> </span><span class="mf">4</span><span class="p">,</span> +<span class="w"> </span><span class="p">},</span> +<span class="w"> </span><span class="nx">paper_bgcolor</span><span class="o">:</span><span class="w"> </span><span class="s2">"black"</span><span class="p">,</span> +<span class="w"> </span><span class="nx">plot_bgcolor</span><span class="o">:</span><span class="w"> </span><span class="s2">"black"</span><span class="p">,</span> +<span class="w"> </span><span class="p">};</span> +<span class="w"> </span><span class="nx">Plotly</span><span class="p">.</span><span class="nx">newPlot</span><span class="p">(</span><span class="s2">"plot"</span><span class="p">,[</span><span class="nx">traceSun</span><span class="p">,</span><span class="nx">traceEarth</span><span class="p">,</span><span class="nx">traceOrbit</span><span class="p">],</span><span class="w"> </span><span class="nx">earthSunLayout</span><span class="p">);</span> +</code></pre> +</div> <h2>Figure of 8 orbit</h2> @@ -240,78 +241,78 @@ Next, the function dR takes the position r and velocity v of Earth as input and <p>The code for this simulation is very similar to the Earth-Sun orbit simulation, except that we now have three bodies instead of two. We also use a different set of initial conditions to generate the figure of 8 orbit.</p> <div class="codehilite"> -<pre><span></span><code><span class="kd">function</span><span class="w"> </span><span class="nx">deltaR</span><span class="p">(</span><span class="nx">coords</span><span class="p">,</span><span class="w"> </span><span class="nx">masses</span><span class="p">,</span><span class="w"> </span><span class="nx">nBodies</span><span class="p">,</span><span class="w"> </span><span class="nx">G</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"></span> -<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">x</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">coords</span><span class="p">[</span><span class="mf">0</span><span class="p">];</span><span class="w"></span> -<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">y</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">coords</span><span class="p">[</span><span class="mf">1</span><span class="p">];</span><span class="w"></span> -<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">vx</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">coords</span><span class="p">[</span><span class="mf">2</span><span class="p">];</span><span class="w"></span> -<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">vy</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">coords</span><span class="p">[</span><span class="mf">3</span><span class="p">];</span><span class="w"></span> - -<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">delta</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">math</span><span class="p">.</span><span class="nx">clone</span><span class="p">(</span><span class="nx">coords</span><span class="p">);</span><span class="w"></span> - -<span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">nBodies</span><span class="p">;</span><span class="w"> </span><span class="nx">n</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"></span> -<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">xn</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">x</span><span class="p">[</span><span class="nx">n</span><span class="p">];</span><span class="w"></span> -<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">yn</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">y</span><span class="p">[</span><span class="nx">n</span><span class="p">];</span><span class="w"></span> -<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">deltaVx</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0.0</span><span class="p">;</span><span class="w"></span> -<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">deltaVy</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0.0</span><span class="p">;</span><span class="w"></span> - -<span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">nBodies</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"></span> -<span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"></span> -<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">sep</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">sqrt</span><span class="p">(</span><span class="nb">Math</span><span class="p">.</span><span class="nx">pow</span><span class="p">(</span><span class="nx">xn</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">x</span><span class="p">[</span><span class="nx">i</span><span class="p">],</span><span class="w"> </span><span class="mf">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">pow</span><span class="p">(</span><span class="nx">yn</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">y</span><span class="p">[</span><span class="nx">i</span><span class="p">],</span><span class="w"> </span><span class="mf">2</span><span class="p">));</span><span class="w"> </span><span class="c1">// Euclidean distance</span><span class="w"></span> -<span class="w"> </span><span class="nx">deltaVx</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="nx">G</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">masses</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="nx">xn</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">x</span><span class="p">[</span><span class="nx">i</span><span class="p">])</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">pow</span><span class="p">(</span><span class="nx">sep</span><span class="p">,</span><span class="w"> </span><span class="mf">3</span><span class="p">);</span><span class="w"></span> -<span class="w"> </span><span class="nx">deltaVy</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="nx">G</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">masses</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="nx">yn</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">y</span><span class="p">[</span><span class="nx">i</span><span class="p">])</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">pow</span><span class="p">(</span><span class="nx">sep</span><span class="p">,</span><span class="w"> </span><span class="mf">3</span><span class="p">);</span><span class="w"></span> -<span class="w"> </span><span class="p">}</span><span class="w"></span> -<span class="w"> </span><span class="p">}</span><span class="w"></span> - -<span class="w"> </span><span class="nx">delta</span><span class="p">[</span><span class="mf">2</span><span class="p">][</span><span class="nx">n</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">deltaVx</span><span class="p">;</span><span class="w"></span> -<span class="w"> </span><span class="nx">delta</span><span class="p">[</span><span class="mf">3</span><span class="p">][</span><span class="nx">n</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">deltaVy</span><span class="p">;</span><span class="w"></span> -<span class="w"> </span><span class="p">}</span><span class="w"></span> - -<span class="w"> </span><span class="nx">delta</span><span class="p">[</span><span class="mf">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">vx</span><span class="p">;</span><span class="w"></span> -<span class="w"> </span><span class="nx">delta</span><span class="p">[</span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">vy</span><span class="p">;</span><span class="w"></span> - -<span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">delta</span><span class="p">;</span><span class="w"></span> -<span class="p">}</span><span class="w"></span> - -<span class="kd">function</span><span class="w"> </span><span class="nx">step</span><span class="p">(</span><span class="nx">coords</span><span class="p">,</span><span class="w"> </span><span class="nx">masses</span><span class="p">,</span><span class="w"> </span><span class="nx">deltaT</span><span class="p">,</span><span class="w"> </span><span class="nx">nBodies</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">3</span><span class="p">,</span><span class="w"> </span><span class="nx">G</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">6.67408313131313e-11</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"></span> -<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">k1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">math</span><span class="p">.</span><span class="nx">multiply</span><span class="p">(</span><span class="nx">deltaT</span><span class="p">,</span><span class="w"> </span><span class="nx">deltaR</span><span class="p">(</span><span class="nx">coords</span><span class="p">,</span><span class="w"> </span><span class="nx">masses</span><span class="p">,</span><span class="w"> </span><span class="nx">nBodies</span><span class="p">,</span><span class="w"> </span><span class="nx">G</span><span class="p">));</span><span class="w"></span> -<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">k2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">math</span><span class="p">.</span><span class="nx">multiply</span><span class="p">(</span><span class="nx">deltaT</span><span class="p">,</span><span class="w"> </span><span class="nx">deltaR</span><span class="p">(</span><span class="nx">math</span><span class="p">.</span><span class="nx">add</span><span class="p">(</span><span class="nx">coords</span><span class="p">,</span><span class="w"> </span><span class="nx">math</span><span class="p">.</span><span class="nx">multiply</span><span class="p">(</span><span class="nx">k1</span><span class="p">,</span><span class="w"> </span><span class="mf">0.5</span><span class="p">)),</span><span class="w"> </span><span class="nx">masses</span><span class="p">,</span><span class="w"> </span><span class="nx">nBodies</span><span class="p">,</span><span class="w"> </span><span class="nx">G</span><span class="p">));</span><span class="w"></span> -<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">k3</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">math</span><span class="p">.</span><span class="nx">multiply</span><span class="p">(</span><span class="nx">deltaT</span><span class="p">,</span><span class="w"> </span><span class="nx">deltaR</span><span class="p">(</span><span class="nx">math</span><span class="p">.</span><span class="nx">add</span><span class="p">(</span><span class="nx">coords</span><span class="p">,</span><span class="w"> </span><span class="nx">math</span><span class="p">.</span><span class="nx">multiply</span><span class="p">(</span><span class="nx">k2</span><span class="p">,</span><span class="w"> </span><span class="mf">0.5</span><span class="p">)),</span><span class="w"> </span><span class="nx">masses</span><span class="p">,</span><span class="w"> </span><span class="nx">nBodies</span><span class="p">,</span><span class="w"> </span><span class="nx">G</span><span class="p">));</span><span class="w"></span> -<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">k4</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">math</span><span class="p">.</span><span class="nx">multiply</span><span class="p">(</span><span class="nx">deltaT</span><span class="p">,</span><span class="w"> </span><span class="nx">deltaR</span><span class="p">(</span><span class="nx">math</span><span class="p">.</span><span class="nx">add</span><span class="p">(</span><span class="nx">coords</span><span class="p">,</span><span class="w"> </span><span class="nx">k3</span><span class="p">),</span><span class="w"> </span><span class="nx">masses</span><span class="p">,</span><span class="w"> </span><span class="nx">nBodies</span><span class="p">,</span><span class="w"> </span><span class="nx">G</span><span class="p">));</span><span class="w"></span> - -<span class="w"> </span><span class="nx">coords</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">math</span><span class="p">.</span><span class="nx">add</span><span class="p">(</span><span class="nx">coords</span><span class="p">,</span><span class="w"> </span><span class="nx">math</span><span class="p">.</span><span class="nx">multiply</span><span class="p">(</span><span class="nx">math</span><span class="p">.</span><span class="nx">add</span><span class="p">(</span><span class="nx">k1</span><span class="p">,</span><span class="w"> </span><span class="nx">math</span><span class="p">.</span><span class="nx">multiply</span><span class="p">(</span><span class="mf">2.0</span><span class="p">,</span><span class="w"> </span><span class="nx">k2</span><span class="p">),</span><span class="w"> </span><span class="nx">math</span><span class="p">.</span><span class="nx">multiply</span><span class="p">(</span><span class="mf">2.0</span><span class="p">,</span><span class="w"> </span><span class="nx">k3</span><span class="p">),</span><span class="w"> </span><span class="nx">k4</span><span class="p">),</span><span class="w"> </span><span class="mf">1</span><span class="o">/</span><span class="mf">6</span><span class="p">));</span><span class="w"></span> - -<span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">coords</span><span class="p">;</span><span class="w"></span> -<span class="p">}</span><span class="w"></span> - -<span class="w"> </span><span class="c1">// Initial conditions setup</span><span class="w"></span> -<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">M</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="mf">1</span><span class="p">];</span><span class="w"></span> -<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">x</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="o">-</span><span class="mf">0.97000436</span><span class="p">,</span><span class="w"> </span><span class="mf">0.0</span><span class="p">,</span><span class="w"> </span><span class="mf">0.97000436</span><span class="p">];</span><span class="w"></span> -<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">y</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="mf">0.24208753</span><span class="p">,</span><span class="w"> </span><span class="mf">0.0</span><span class="p">,</span><span class="w"> </span><span class="o">-</span><span class="mf">0.24208753</span><span class="p">];</span><span class="w"></span> -<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">vx</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="mf">0.4662036850</span><span class="p">,</span><span class="w"> </span><span class="o">-</span><span class="mf">0.933240737</span><span class="p">,</span><span class="w"> </span><span class="mf">0.4662036850</span><span class="p">];</span><span class="w"></span> -<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">vy</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="mf">0.4323657300</span><span class="p">,</span><span class="w"> </span><span class="o">-</span><span class="mf">0.86473146</span><span class="p">,</span><span class="w"> </span><span class="mf">0.4323657300</span><span class="p">];</span><span class="w"></span> -<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">Ei</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">-</span><span class="mf">1</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">sqrt</span><span class="p">(</span><span class="nb">Math</span><span class="p">.</span><span class="nx">pow</span><span class="p">(</span><span class="mf">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mf">0.97000436</span><span class="p">,</span><span class="w"> </span><span class="mf">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">pow</span><span class="p">(</span><span class="mf">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mf">0.24208753</span><span class="p">,</span><span class="w"> </span><span class="mf">2</span><span class="p">))</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">sqrt</span><span class="p">(</span><span class="nb">Math</span><span class="p">.</span><span class="nx">pow</span><span class="p">(</span><span class="mf">0.97000436</span><span class="p">,</span><span class="w"> </span><span class="mf">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">pow</span><span class="p">(</span><span class="mf">0.24208753</span><span class="p">,</span><span class="w"> </span><span class="mf">2</span><span class="p">))</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">0.5</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="nx">math</span><span class="p">.</span><span class="nx">sum</span><span class="p">(</span><span class="nx">math</span><span class="p">.</span><span class="nx">add</span><span class="p">(</span><span class="nx">math</span><span class="p">.</span><span class="nx">dotPow</span><span class="p">(</span><span class="nx">vx</span><span class="p">,</span><span class="w"> </span><span class="mf">2</span><span class="p">),</span><span class="w"> </span><span class="nx">math</span><span class="p">.</span><span class="nx">dotPow</span><span class="p">(</span><span class="nx">vy</span><span class="p">,</span><span class="w"> </span><span class="mf">2</span><span class="p">))));</span><span class="w"></span> - -<span class="w"> </span><span class="kd">function</span><span class="w"> </span><span class="nx">linspace</span><span class="p">(</span><span class="nx">start</span><span class="p">,</span><span class="w"> </span><span class="nx">stop</span><span class="p">,</span><span class="w"> </span><span class="nx">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"></span> -<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">step</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="nx">stop</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">start</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="p">(</span><span class="nx">num</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span><span class="w"></span> -<span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nb">Array</span><span class="p">.</span><span class="kr">from</span><span class="p">({</span><span class="nx">length</span><span class="o">:</span><span class="w"> </span><span class="nx">num</span><span class="p">},</span><span class="w"> </span><span class="p">(</span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="nx">start</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="nx">step</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">i</span><span class="p">));</span><span class="w"></span> -<span class="w"> </span><span class="p">}</span><span class="w"></span> - -<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">coords</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="nx">x</span><span class="p">,</span><span class="w"> </span><span class="nx">y</span><span class="p">,</span><span class="w"> </span><span class="nx">vx</span><span class="p">,</span><span class="w"> </span><span class="nx">vy</span><span class="p">];</span><span class="w"></span> -<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">time</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">linspace</span><span class="p">(</span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="mf">6.3259</span><span class="p">,</span><span class="w"> </span><span class="mf">1001</span><span class="p">);</span><span class="w"></span> -<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">deltaT</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">time</span><span class="p">[</span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">time</span><span class="p">[</span><span class="mf">0</span><span class="p">];</span><span class="w"></span> - -<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">X</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">math</span><span class="p">.</span><span class="nx">zeros</span><span class="p">(</span><span class="mf">3</span><span class="p">,</span><span class="w"> </span><span class="nx">time</span><span class="p">.</span><span class="nx">length</span><span class="p">).</span><span class="nx">toArray</span><span class="p">();</span><span class="w"></span> -<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">Y</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">math</span><span class="p">.</span><span class="nx">zeros</span><span class="p">(</span><span class="mf">3</span><span class="p">,</span><span class="w"> </span><span class="nx">time</span><span class="p">.</span><span class="nx">length</span><span class="p">).</span><span class="nx">toArray</span><span class="p">();</span><span class="w"></span> -<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">VX</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">math</span><span class="p">.</span><span class="nx">zeros</span><span class="p">(</span><span class="mf">3</span><span class="p">,</span><span class="w"> </span><span class="nx">time</span><span class="p">.</span><span class="nx">length</span><span class="p">).</span><span class="nx">toArray</span><span class="p">();</span><span class="w"></span> -<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">VY</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">math</span><span class="p">.</span><span class="nx">zeros</span><span class="p">(</span><span class="mf">3</span><span class="p">,</span><span class="w"> </span><span class="nx">time</span><span class="p">.</span><span class="nx">length</span><span class="p">).</span><span class="nx">toArray</span><span class="p">();</span><span class="w"></span> - -<span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">time</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"></span> -<span class="w"> </span><span class="nx">coords</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">step</span><span class="p">(</span><span class="nx">coords</span><span class="p">,</span><span class="w"> </span><span class="nx">M</span><span class="p">,</span><span class="w"> </span><span class="nx">deltaT</span><span class="p">,</span><span class="w"> </span><span class="mf">3</span><span class="p">,</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span><span class="w"></span> -<span class="w"> </span><span class="nx">X</span><span class="p">.</span><span class="nx">forEach</span><span class="p">((</span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">idx</span><span class="p">)</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="nx">X</span><span class="p">[</span><span class="nx">idx</span><span class="p">][</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">coords</span><span class="p">[</span><span class="mf">0</span><span class="p">][</span><span class="nx">idx</span><span class="p">]);</span><span class="w"></span> -<span class="w"> </span><span class="nx">Y</span><span class="p">.</span><span class="nx">forEach</span><span class="p">((</span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">idx</span><span class="p">)</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="nx">Y</span><span class="p">[</span><span class="nx">idx</span><span class="p">][</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">coords</span><span class="p">[</span><span class="mf">1</span><span class="p">][</span><span class="nx">idx</span><span class="p">]);</span><span class="w"></span> -<span class="w"> </span><span class="nx">VX</span><span class="p">.</span><span class="nx">forEach</span><span class="p">((</span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">idx</span><span class="p">)</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="nx">VX</span><span class="p">[</span><span class="nx">idx</span><span class="p">][</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">coords</span><span class="p">[</span><span class="mf">2</span><span class="p">][</span><span class="nx">idx</span><span class="p">]);</span><span class="w"></span> -<span class="w"> </span><span class="nx">VY</span><span class="p">.</span><span class="nx">forEach</span><span class="p">((</span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">idx</span><span class="p">)</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="nx">VY</span><span class="p">[</span><span class="nx">idx</span><span class="p">][</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">coords</span><span class="p">[</span><span class="mf">3</span><span class="p">][</span><span class="nx">idx</span><span class="p">]);</span><span class="w"></span> -<span class="w"> </span><span class="p">}</span><span class="w"></span> +<pre><span></span><code><span class="kd">function</span><span class="w"> </span><span class="nx">deltaR</span><span class="p">(</span><span class="nx">coords</span><span class="p">,</span><span class="w"> </span><span class="nx">masses</span><span class="p">,</span><span class="w"> </span><span class="nx">nBodies</span><span class="p">,</span><span class="w"> </span><span class="nx">G</span><span class="p">)</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">x</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">coords</span><span class="p">[</span><span class="mf">0</span><span class="p">];</span> +<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">y</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">coords</span><span class="p">[</span><span class="mf">1</span><span class="p">];</span> +<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">vx</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">coords</span><span class="p">[</span><span class="mf">2</span><span class="p">];</span> +<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">vy</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">coords</span><span class="p">[</span><span class="mf">3</span><span class="p">];</span> + +<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">delta</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">math</span><span class="p">.</span><span class="nx">clone</span><span class="p">(</span><span class="nx">coords</span><span class="p">);</span> + +<span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">nBodies</span><span class="p">;</span><span class="w"> </span><span class="nx">n</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">xn</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">x</span><span class="p">[</span><span class="nx">n</span><span class="p">];</span> +<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">yn</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">y</span><span class="p">[</span><span class="nx">n</span><span class="p">];</span> +<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">deltaVx</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0.0</span><span class="p">;</span> +<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">deltaVy</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0.0</span><span class="p">;</span> + +<span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">nBodies</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">sep</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">sqrt</span><span class="p">(</span><span class="nb">Math</span><span class="p">.</span><span class="nx">pow</span><span class="p">(</span><span class="nx">xn</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">x</span><span class="p">[</span><span class="nx">i</span><span class="p">],</span><span class="w"> </span><span class="mf">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">pow</span><span class="p">(</span><span class="nx">yn</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">y</span><span class="p">[</span><span class="nx">i</span><span class="p">],</span><span class="w"> </span><span class="mf">2</span><span class="p">));</span><span class="w"> </span><span class="c1">// Euclidean distance</span> +<span class="w"> </span><span class="nx">deltaVx</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="nx">G</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">masses</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="nx">xn</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">x</span><span class="p">[</span><span class="nx">i</span><span class="p">])</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">pow</span><span class="p">(</span><span class="nx">sep</span><span class="p">,</span><span class="w"> </span><span class="mf">3</span><span class="p">);</span> +<span class="w"> </span><span class="nx">deltaVy</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="nx">G</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">masses</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="nx">yn</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">y</span><span class="p">[</span><span class="nx">i</span><span class="p">])</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">pow</span><span class="p">(</span><span class="nx">sep</span><span class="p">,</span><span class="w"> </span><span class="mf">3</span><span class="p">);</span> +<span class="w"> </span><span class="p">}</span> +<span class="w"> </span><span class="p">}</span> + +<span class="w"> </span><span class="nx">delta</span><span class="p">[</span><span class="mf">2</span><span class="p">][</span><span class="nx">n</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">deltaVx</span><span class="p">;</span> +<span class="w"> </span><span class="nx">delta</span><span class="p">[</span><span class="mf">3</span><span class="p">][</span><span class="nx">n</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">deltaVy</span><span class="p">;</span> +<span class="w"> </span><span class="p">}</span> + +<span class="w"> </span><span class="nx">delta</span><span class="p">[</span><span class="mf">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">vx</span><span class="p">;</span> +<span class="w"> </span><span class="nx">delta</span><span class="p">[</span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">vy</span><span class="p">;</span> + +<span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">delta</span><span class="p">;</span> +<span class="p">}</span> + +<span class="kd">function</span><span class="w"> </span><span class="nx">step</span><span class="p">(</span><span class="nx">coords</span><span class="p">,</span><span class="w"> </span><span class="nx">masses</span><span class="p">,</span><span class="w"> </span><span class="nx">deltaT</span><span class="p">,</span><span class="w"> </span><span class="nx">nBodies</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">3</span><span class="p">,</span><span class="w"> </span><span class="nx">G</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">6.67408313131313e-11</span><span class="p">)</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">k1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">math</span><span class="p">.</span><span class="nx">multiply</span><span class="p">(</span><span class="nx">deltaT</span><span class="p">,</span><span class="w"> </span><span class="nx">deltaR</span><span class="p">(</span><span class="nx">coords</span><span class="p">,</span><span class="w"> </span><span class="nx">masses</span><span class="p">,</span><span class="w"> </span><span class="nx">nBodies</span><span class="p">,</span><span class="w"> </span><span class="nx">G</span><span class="p">));</span> +<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">k2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">math</span><span class="p">.</span><span class="nx">multiply</span><span class="p">(</span><span class="nx">deltaT</span><span class="p">,</span><span class="w"> </span><span class="nx">deltaR</span><span class="p">(</span><span class="nx">math</span><span class="p">.</span><span class="nx">add</span><span class="p">(</span><span class="nx">coords</span><span class="p">,</span><span class="w"> </span><span class="nx">math</span><span class="p">.</span><span class="nx">multiply</span><span class="p">(</span><span class="nx">k1</span><span class="p">,</span><span class="w"> </span><span class="mf">0.5</span><span class="p">)),</span><span class="w"> </span><span class="nx">masses</span><span class="p">,</span><span class="w"> </span><span class="nx">nBodies</span><span class="p">,</span><span class="w"> </span><span class="nx">G</span><span class="p">));</span> +<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">k3</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">math</span><span class="p">.</span><span class="nx">multiply</span><span class="p">(</span><span class="nx">deltaT</span><span class="p">,</span><span class="w"> </span><span class="nx">deltaR</span><span class="p">(</span><span class="nx">math</span><span class="p">.</span><span class="nx">add</span><span class="p">(</span><span class="nx">coords</span><span class="p">,</span><span class="w"> </span><span class="nx">math</span><span class="p">.</span><span class="nx">multiply</span><span class="p">(</span><span class="nx">k2</span><span class="p">,</span><span class="w"> </span><span class="mf">0.5</span><span class="p">)),</span><span class="w"> </span><span class="nx">masses</span><span class="p">,</span><span class="w"> </span><span class="nx">nBodies</span><span class="p">,</span><span class="w"> </span><span class="nx">G</span><span class="p">));</span> +<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">k4</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">math</span><span class="p">.</span><span class="nx">multiply</span><span class="p">(</span><span class="nx">deltaT</span><span class="p">,</span><span class="w"> </span><span class="nx">deltaR</span><span class="p">(</span><span class="nx">math</span><span class="p">.</span><span class="nx">add</span><span class="p">(</span><span class="nx">coords</span><span class="p">,</span><span class="w"> </span><span class="nx">k3</span><span class="p">),</span><span class="w"> </span><span class="nx">masses</span><span class="p">,</span><span class="w"> </span><span class="nx">nBodies</span><span class="p">,</span><span class="w"> </span><span class="nx">G</span><span class="p">));</span> + +<span class="w"> </span><span class="nx">coords</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">math</span><span class="p">.</span><span class="nx">add</span><span class="p">(</span><span class="nx">coords</span><span class="p">,</span><span class="w"> </span><span class="nx">math</span><span class="p">.</span><span class="nx">multiply</span><span class="p">(</span><span class="nx">math</span><span class="p">.</span><span class="nx">add</span><span class="p">(</span><span class="nx">k1</span><span class="p">,</span><span class="w"> </span><span class="nx">math</span><span class="p">.</span><span class="nx">multiply</span><span class="p">(</span><span class="mf">2.0</span><span class="p">,</span><span class="w"> </span><span class="nx">k2</span><span class="p">),</span><span class="w"> </span><span class="nx">math</span><span class="p">.</span><span class="nx">multiply</span><span class="p">(</span><span class="mf">2.0</span><span class="p">,</span><span class="w"> </span><span class="nx">k3</span><span class="p">),</span><span class="w"> </span><span class="nx">k4</span><span class="p">),</span><span class="w"> </span><span class="mf">1</span><span class="o">/</span><span class="mf">6</span><span class="p">));</span> + +<span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">coords</span><span class="p">;</span> +<span class="p">}</span> + +<span class="w"> </span><span class="c1">// Initial conditions setup</span> +<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">M</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="mf">1</span><span class="p">];</span> +<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">x</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="o">-</span><span class="mf">0.97000436</span><span class="p">,</span><span class="w"> </span><span class="mf">0.0</span><span class="p">,</span><span class="w"> </span><span class="mf">0.97000436</span><span class="p">];</span> +<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">y</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="mf">0.24208753</span><span class="p">,</span><span class="w"> </span><span class="mf">0.0</span><span class="p">,</span><span class="w"> </span><span class="o">-</span><span class="mf">0.24208753</span><span class="p">];</span> +<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">vx</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="mf">0.4662036850</span><span class="p">,</span><span class="w"> </span><span class="o">-</span><span class="mf">0.933240737</span><span class="p">,</span><span class="w"> </span><span class="mf">0.4662036850</span><span class="p">];</span> +<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">vy</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="mf">0.4323657300</span><span class="p">,</span><span class="w"> </span><span class="o">-</span><span class="mf">0.86473146</span><span class="p">,</span><span class="w"> </span><span class="mf">0.4323657300</span><span class="p">];</span> +<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">Ei</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">-</span><span class="mf">1</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">sqrt</span><span class="p">(</span><span class="nb">Math</span><span class="p">.</span><span class="nx">pow</span><span class="p">(</span><span class="mf">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mf">0.97000436</span><span class="p">,</span><span class="w"> </span><span class="mf">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">pow</span><span class="p">(</span><span class="mf">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mf">0.24208753</span><span class="p">,</span><span class="w"> </span><span class="mf">2</span><span class="p">))</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">sqrt</span><span class="p">(</span><span class="nb">Math</span><span class="p">.</span><span class="nx">pow</span><span class="p">(</span><span class="mf">0.97000436</span><span class="p">,</span><span class="w"> </span><span class="mf">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">pow</span><span class="p">(</span><span class="mf">0.24208753</span><span class="p">,</span><span class="w"> </span><span class="mf">2</span><span class="p">))</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">0.5</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="nx">math</span><span class="p">.</span><span class="nx">sum</span><span class="p">(</span><span class="nx">math</span><span class="p">.</span><span class="nx">add</span><span class="p">(</span><span class="nx">math</span><span class="p">.</span><span class="nx">dotPow</span><span class="p">(</span><span class="nx">vx</span><span class="p">,</span><span class="w"> </span><span class="mf">2</span><span class="p">),</span><span class="w"> </span><span class="nx">math</span><span class="p">.</span><span class="nx">dotPow</span><span class="p">(</span><span class="nx">vy</span><span class="p">,</span><span class="w"> </span><span class="mf">2</span><span class="p">))));</span> + +<span class="w"> </span><span class="kd">function</span><span class="w"> </span><span class="nx">linspace</span><span class="p">(</span><span class="nx">start</span><span class="p">,</span><span class="w"> </span><span class="nx">stop</span><span class="p">,</span><span class="w"> </span><span class="nx">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">step</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="nx">stop</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">start</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="p">(</span><span class="nx">num</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span> +<span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nb">Array</span><span class="p">.</span><span class="kr">from</span><span class="p">({</span><span class="nx">length</span><span class="o">:</span><span class="w"> </span><span class="nx">num</span><span class="p">},</span><span class="w"> </span><span class="p">(</span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="nx">start</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="nx">step</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">i</span><span class="p">));</span> +<span class="w"> </span><span class="p">}</span> + +<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">coords</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="nx">x</span><span class="p">,</span><span class="w"> </span><span class="nx">y</span><span class="p">,</span><span class="w"> </span><span class="nx">vx</span><span class="p">,</span><span class="w"> </span><span class="nx">vy</span><span class="p">];</span> +<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">time</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">linspace</span><span class="p">(</span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="mf">6.3259</span><span class="p">,</span><span class="w"> </span><span class="mf">1001</span><span class="p">);</span> +<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">deltaT</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">time</span><span class="p">[</span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">time</span><span class="p">[</span><span class="mf">0</span><span class="p">];</span> + +<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">X</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">math</span><span class="p">.</span><span class="nx">zeros</span><span class="p">(</span><span class="mf">3</span><span class="p">,</span><span class="w"> </span><span class="nx">time</span><span class="p">.</span><span class="nx">length</span><span class="p">).</span><span class="nx">toArray</span><span class="p">();</span> +<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">Y</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">math</span><span class="p">.</span><span class="nx">zeros</span><span class="p">(</span><span class="mf">3</span><span class="p">,</span><span class="w"> </span><span class="nx">time</span><span class="p">.</span><span class="nx">length</span><span class="p">).</span><span class="nx">toArray</span><span class="p">();</span> +<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">VX</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">math</span><span class="p">.</span><span class="nx">zeros</span><span class="p">(</span><span class="mf">3</span><span class="p">,</span><span class="w"> </span><span class="nx">time</span><span class="p">.</span><span class="nx">length</span><span class="p">).</span><span class="nx">toArray</span><span class="p">();</span> +<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">VY</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">math</span><span class="p">.</span><span class="nx">zeros</span><span class="p">(</span><span class="mf">3</span><span class="p">,</span><span class="w"> </span><span class="nx">time</span><span class="p">.</span><span class="nx">length</span><span class="p">).</span><span class="nx">toArray</span><span class="p">();</span> + +<span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">time</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="nx">coords</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">step</span><span class="p">(</span><span class="nx">coords</span><span class="p">,</span><span class="w"> </span><span class="nx">M</span><span class="p">,</span><span class="w"> </span><span class="nx">deltaT</span><span class="p">,</span><span class="w"> </span><span class="mf">3</span><span class="p">,</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span> +<span class="w"> </span><span class="nx">X</span><span class="p">.</span><span class="nx">forEach</span><span class="p">((</span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">idx</span><span class="p">)</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="nx">X</span><span class="p">[</span><span class="nx">idx</span><span class="p">][</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">coords</span><span class="p">[</span><span class="mf">0</span><span class="p">][</span><span class="nx">idx</span><span class="p">]);</span> +<span class="w"> </span><span class="nx">Y</span><span class="p">.</span><span class="nx">forEach</span><span class="p">((</span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">idx</span><span class="p">)</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="nx">Y</span><span class="p">[</span><span class="nx">idx</span><span class="p">][</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">coords</span><span class="p">[</span><span class="mf">1</span><span class="p">][</span><span class="nx">idx</span><span class="p">]);</span> +<span class="w"> </span><span class="nx">VX</span><span class="p">.</span><span class="nx">forEach</span><span class="p">((</span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">idx</span><span class="p">)</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="nx">VX</span><span class="p">[</span><span class="nx">idx</span><span class="p">][</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">coords</span><span class="p">[</span><span class="mf">2</span><span class="p">][</span><span class="nx">idx</span><span class="p">]);</span> +<span class="w"> </span><span class="nx">VY</span><span class="p">.</span><span class="nx">forEach</span><span class="p">((</span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">idx</span><span class="p">)</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="nx">VY</span><span class="p">[</span><span class="nx">idx</span><span class="p">][</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">coords</span><span class="p">[</span><span class="mf">3</span><span class="p">][</span><span class="nx">idx</span><span class="p">]);</span> +<span class="w"> </span><span class="p">}</span> </code></pre> </div> @@ -329,365 +330,369 @@ Next, the function dR takes the position r and velocity v of Earth as input and <h3>Animation?</h3> -<p>Now that we have time-series data, we need to animate it. We can use Plotly's animate function, as this does not force a full re-render, saving us some precious GPU and CPU cycles when we are trying to run this in the browser itself - <div class="codehilite"> - <pre><span></span><code><span class="kd">function</span><span class="w"> </span><span class="nx">plotClassicFunc</span><span class="p">()</span><span class="w"> </span><span class="p">{</span><span class="w"></span> - <span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nx">tailLength</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"></span> - <span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">plotIndex</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">tailLength</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"></span> - <span class="w"> </span><span class="nx">tailLength</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"></span> - <span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">plotIndex</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="nx">time</span><span class="p">.</span><span class="nx">length</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"></span> - <span class="w"> </span><span class="nx">plotIndex</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"></span> - <span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span><span class="w"></span> - <span class="w"> </span><span class="nx">tailLength</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">plotIndex</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">tailLength</span><span class="p">;</span><span class="w"></span> - <span class="w"> </span><span class="p">}</span><span class="w"></span> - <br /> - <span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nx">currentIndex</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">plotIndex</span><span class="p">;</span><span class="w"></span> - <br /> - <span class="w"> </span><span class="k">try</span><span class="w"> </span><span class="p">{</span><span class="w"></span> - <span class="w"> </span><span class="nx">time</span><span class="p">[</span><span class="nx">currentIndex</span><span class="p">].</span><span class="nx">toFixed</span><span class="p">(</span><span class="mf">3</span><span class="p">);</span><span class="w"></span> - <span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">catch</span><span class="w"> </span><span class="p">(</span><span class="nx">e</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"></span> - <span class="w"> </span><span class="nx">currentIndex</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"></span> - <span class="w"> </span><span class="p">}</span><span class="w"></span> - <br /> - <span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">data</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="w"></span> - <span class="w"> </span><span class="p">{</span><span class="w"></span> - <span class="w"> </span><span class="nx">x</span><span class="o">:</span><span class="w"> </span><span class="nx">X</span><span class="p">[</span><span class="mf">0</span><span class="p">].</span><span class="nx">slice</span><span class="p">(</span><span class="nx">tailLength</span><span class="p">,</span><span class="w"> </span><span class="nx">currentIndex</span><span class="p">),</span><span class="w"></span> - <span class="w"> </span><span class="nx">y</span><span class="o">:</span><span class="w"> </span><span class="nx">Y</span><span class="p">[</span><span class="mf">0</span><span class="p">].</span><span class="nx">slice</span><span class="p">(</span><span class="nx">tailLength</span><span class="p">,</span><span class="w"> </span><span class="nx">currentIndex</span><span class="p">),</span><span class="w"></span> - <span class="w"> </span><span class="nx">mode</span><span class="o">:</span><span class="w"> </span><span class="s1">'lines+markers'</span><span class="p">,</span><span class="w"></span> - <span class="w"> </span><span class="nx">marker</span><span class="o">:</span><span class="w"> </span><span class="p">{</span><span class="w"></span> - <span class="w"> </span><span class="nx">symbol</span><span class="o">:</span><span class="w"> </span><span class="s1">'star'</span><span class="p">,</span><span class="w"></span> - <span class="w"> </span><span class="nx">size</span><span class="o">:</span><span class="w"> </span><span class="mf">8</span><span class="p">,</span><span class="w"></span> - <span class="w"> </span><span class="nx">line</span><span class="o">:</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nx">width</span><span class="o">:</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="p">},</span><span class="w"></span> - <span class="w"> </span><span class="p">},</span><span class="w"></span> - <span class="w"> </span><span class="nx">line</span><span class="o">:</span><span class="w"> </span><span class="p">{</span><span class="w"></span> - <span class="w"> </span><span class="nx">width</span><span class="o">:</span><span class="w"> </span><span class="mf">2</span><span class="p">,</span><span class="w"></span> - <span class="w"> </span><span class="p">},</span><span class="w"></span> - <span class="w"> </span><span class="nx">name</span><span class="o">:</span><span class="w"> </span><span class="s1">''</span><span class="p">,</span><span class="w"></span> - <span class="w"> </span><span class="p">},</span><span class="w"></span> - <span class="w"> </span><span class="p">{</span><span class="w"></span> - <span class="w"> </span><span class="nx">x</span><span class="o">:</span><span class="w"> </span><span class="nx">X</span><span class="p">[</span><span class="mf">1</span><span class="p">].</span><span class="nx">slice</span><span class="p">(</span><span class="nx">tailLength</span><span class="p">,</span><span class="w"> </span><span class="nx">currentIndex</span><span class="p">),</span><span class="w"></span> - <span class="w"> </span><span class="nx">y</span><span class="o">:</span><span class="w"> </span><span class="nx">Y</span><span class="p">[</span><span class="mf">1</span><span class="p">].</span><span class="nx">slice</span><span class="p">(</span><span class="nx">tailLength</span><span class="p">,</span><span class="w"> </span><span class="nx">currentIndex</span><span class="p">),</span><span class="w"></span> - <span class="w"> </span><span class="nx">mode</span><span class="o">:</span><span class="w"> </span><span class="s1">'lines+markers'</span><span class="p">,</span><span class="w"></span> - <span class="w"> </span><span class="nx">marker</span><span class="o">:</span><span class="w"> </span><span class="p">{</span><span class="w"></span> - <span class="w"> </span><span class="nx">symbol</span><span class="o">:</span><span class="w"> </span><span class="s1">'star'</span><span class="p">,</span><span class="w"></span> - <span class="w"> </span><span class="nx">size</span><span class="o">:</span><span class="w"> </span><span class="mf">8</span><span class="p">,</span><span class="w"></span> - <span class="w"> </span><span class="nx">line</span><span class="o">:</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nx">width</span><span class="o">:</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="p">},</span><span class="w"></span> - <span class="w"> </span><span class="p">},</span><span class="w"></span> - <span class="w"> </span><span class="nx">line</span><span class="o">:</span><span class="w"> </span><span class="p">{</span><span class="w"></span> - <span class="w"> </span><span class="nx">width</span><span class="o">:</span><span class="w"> </span><span class="mf">2</span><span class="p">,</span><span class="w"></span> - <span class="w"> </span><span class="p">},</span><span class="w"></span> - <span class="w"> </span><span class="nx">name</span><span class="o">:</span><span class="w"> </span><span class="s1">''</span><span class="p">,</span><span class="w"></span> - <span class="w"> </span><span class="p">},</span><span class="w"></span> - <span class="w"> </span><span class="p">{</span><span class="w"></span> - <span class="w"> </span><span class="nx">x</span><span class="o">:</span><span class="w"> </span><span class="nx">X</span><span class="p">[</span><span class="mf">2</span><span class="p">].</span><span class="nx">slice</span><span class="p">(</span><span class="nx">tailLength</span><span class="p">,</span><span class="w"> </span><span class="nx">currentIndex</span><span class="p">),</span><span class="w"></span> - <span class="w"> </span><span class="nx">y</span><span class="o">:</span><span class="w"> </span><span class="nx">Y</span><span class="p">[</span><span class="mf">2</span><span class="p">].</span><span class="nx">slice</span><span class="p">(</span><span class="nx">tailLength</span><span class="p">,</span><span class="w"> </span><span class="nx">currentIndex</span><span class="p">),</span><span class="w"></span> - <span class="w"> </span><span class="nx">mode</span><span class="o">:</span><span class="w"> </span><span class="s1">'lines+markers'</span><span class="p">,</span><span class="w"></span> - <span class="w"> </span><span class="nx">marker</span><span class="o">:</span><span class="w"> </span><span class="p">{</span><span class="w"></span> - <span class="w"> </span><span class="nx">symbol</span><span class="o">:</span><span class="w"> </span><span class="s1">'star'</span><span class="p">,</span><span class="w"></span> - <span class="w"> </span><span class="nx">size</span><span class="o">:</span><span class="w"> </span><span class="mf">8</span><span class="p">,</span><span class="w"></span> - <span class="w"> </span><span class="nx">line</span><span class="o">:</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nx">width</span><span class="o">:</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="p">},</span><span class="w"></span> - <span class="w"> </span><span class="p">},</span><span class="w"></span> - <span class="w"> </span><span class="nx">line</span><span class="o">:</span><span class="w"> </span><span class="p">{</span><span class="w"></span> - <span class="w"> </span><span class="nx">width</span><span class="o">:</span><span class="w"> </span><span class="mf">2</span><span class="p">,</span><span class="w"></span> - <span class="w"> </span><span class="p">},</span><span class="w"></span> - <span class="w"> </span><span class="nx">name</span><span class="o">:</span><span class="w"> </span><span class="s1">''</span><span class="p">,</span><span class="w"></span> - <span class="w"> </span><span class="p">},</span><span class="w"></span> - <span class="p">];</span><span class="w"></span> - <br /> - <span class="c1">// width: 1000, height: 400</span><span class="w"></span> - <span class="kd">const</span><span class="w"> </span><span class="nx">layout</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="w"></span> - <span class="w"> </span><span class="nx">title</span><span class="o">:</span><span class="w"> </span><span class="s1">'∞ Three-Body Problem: t = '</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">time</span><span class="p">[</span><span class="nx">currentIndex</span><span class="p">].</span><span class="nx">toFixed</span><span class="p">(</span><span class="mf">3</span><span class="p">),</span><span class="w"></span> - <span class="w"> </span><span class="nx">xaxis</span><span class="o">:</span><span class="w"> </span><span class="p">{</span><span class="w"></span> - <span class="w"> </span><span class="nx">title</span><span class="o">:</span><span class="w"> </span><span class="s1">'x'</span><span class="p">,</span><span class="w"></span> - <span class="w"> </span><span class="nx">range</span><span class="o">:</span><span class="w"> </span><span class="p">[</span><span class="o">-</span><span class="mf">1.1</span><span class="p">,</span><span class="mf">1.1</span><span class="p">]</span><span class="w"></span> - <span class="w"> </span><span class="p">},</span><span class="w"></span> - <span class="w"> </span><span class="nx">yaxis</span><span class="o">:</span><span class="w"> </span><span class="p">{</span><span class="w"></span> - <span class="w"> </span><span class="nx">title</span><span class="o">:</span><span class="w"> </span><span class="s1">'y'</span><span class="p">,</span><span class="w"></span> - <span class="w"> </span><span class="nx">scaleanchor</span><span class="o">:</span><span class="w"> </span><span class="s1">'x'</span><span class="p">,</span><span class="w"></span> - <span class="w"> </span><span class="nx">scaleratio</span><span class="o">:</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span><span class="w"></span> - <span class="w"> </span><span class="nx">range</span><span class="o">:</span><span class="w"> </span><span class="p">[</span><span class="o">-</span><span class="mf">0.5</span><span class="p">,</span><span class="mf">0.5</span><span class="p">]</span><span class="w"></span> - <span class="w"> </span><span class="p">},</span><span class="w"></span> - <span class="w"> </span><span class="nx">plot<em>bgcolor</span><span class="o">:</span><span class="w"> </span><span class="s1">'black'</span><span class="p">,</span><span class="w"></span> - <span class="w"> </span><span class="nx">paper</em>bgcolor</span><span class="o">:</span><span class="w"> </span><span class="s1">'black'</span><span class="p">,</span><span class="w"></span> - <span class="w"> </span><span class="nx">font</span><span class="o">:</span><span class="w"> </span><span class="p">{</span><span class="w"></span> - <span class="w"> </span><span class="nx">color</span><span class="o">:</span><span class="w"> </span><span class="s1">'white'</span><span class="p">,</span><span class="w"></span> - <span class="w"> </span><span class="p">},</span><span class="w"></span> - <span class="p">};</span><span class="w"></span> - <br /> - <span class="k">try</span><span class="w"> </span><span class="p">{</span><span class="w"></span> - <span class="nx">Plotly</span><span class="p">.</span><span class="nx">animate</span><span class="p">(</span><span class="s2">"plot"</span><span class="p">,</span><span class="w"> </span><span class="p">{</span><span class="w"></span> - <span class="w"> </span><span class="nx">data</span><span class="o">:</span><span class="w"> </span><span class="nx">data</span><span class="p">,</span><span class="w"> </span><span class="nx">layout</span><span class="o">:</span><span class="w"> </span><span class="nx">layout</span><span class="w"></span> - <span class="w"> </span><span class="p">},</span><span class="w"> </span><span class="p">{</span><span class="w"></span> - <span class="w"> </span><span class="nx">staticPlot</span><span class="o">:</span><span class="w"> </span><span class="kc">true</span><span class="p">,</span><span class="w"></span> - <span class="w"> </span><span class="nx">transition</span><span class="o">:</span><span class="w"> </span><span class="p">{</span><span class="w"></span> - <span class="w"> </span><span class="nx">duration</span><span class="o">:</span><span class="w"> </span><span class="mf">0</span><span class="p">,</span><span class="w"></span> - <span class="w"> </span><span class="p">},</span><span class="w"></span> - <span class="w"> </span><span class="nx">frame</span><span class="o">:</span><span class="w"> </span><span class="p">{</span><span class="w"></span> - <span class="w"> </span><span class="nx">duration</span><span class="o">:</span><span class="w"> </span><span class="mf">0</span><span class="p">,</span><span class="w"></span> - <span class="w"> </span><span class="nx">redraw</span><span class="o">:</span><span class="w"> </span><span class="kc">false</span><span class="p">,</span><span class="w"></span> - <span class="w"> </span><span class="p">}</span><span class="w"></span> - <span class="w"> </span><span class="p">});</span><span class="w"></span> - <span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">catch</span><span class="w"> </span><span class="p">(</span><span class="nx">err</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"></span> - <span class="w"> </span><span class="nx">Plotly</span><span class="p">.</span><span class="nx">newPlot</span><span class="p">(</span><span class="s1">'plot'</span><span class="p">,</span><span class="w"> </span><span class="nx">data</span><span class="p">,</span><span class="w"> </span><span class="nx">layout</span><span class="p">);</span><span class="w"></span> - <span class="w"> </span><span class="p">}</span><span class="w"></span> - <br /> - <br /> - <span class="nx">plotIndex</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="nx">delay</span><span class="p">;</span><span class="w"></span> - <span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">plotClassic</span><span class="o">===</span><span class="kc">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"></span> - <span class="w"> </span><span class="k">try</span><span class="w"> </span><span class="p">{</span><span class="w"></span> - <span class="w"> </span><span class="nx">requestAnimationFrame</span><span class="p">(</span><span class="nx">plotClassicFunc</span><span class="p">);</span><span class="w"></span> - <span class="w"> </span><span class="p">}</span><span class="w"></span> - <span class="w"> </span><span class="k">catch</span><span class="w"> </span><span class="p">(</span><span class="nx">err</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"></span> - <span class="w"> </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="nx">err</span><span class="p">)</span><span class="w"></span> - <span class="w"> </span><span class="p">}</span><span class="w"></span> - <span class="p">}</span><span class="w"></span> - <br /> - <span class="p">}</span><span class="w"></span> - </code></pre> - </div></p> +<p>Now that we have time-series data, we need to animate it. We can use Plotly's animate function, as this does not force a full re-render, saving us some precious GPU and CPU cycles when we are trying to run this in the browser itself</p> + +<div class="codehilite"> +<pre><span></span><code><span class="w"> </span><span class="kd">function</span><span class="w"> </span><span class="nx">plotClassicFunc</span><span class="p">()</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nx">tailLength</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span> +<span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">plotIndex</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">tailLength</span><span class="p">)</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="nx">tailLength</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span> +<span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">plotIndex</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="nx">time</span><span class="p">.</span><span class="nx">length</span><span class="p">)</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="nx">plotIndex</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span> +<span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="nx">tailLength</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">plotIndex</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">tailLength</span><span class="p">;</span> +<span class="w"> </span><span class="p">}</span> + +<span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nx">currentIndex</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">plotIndex</span><span class="p">;</span> + +<span class="w"> </span><span class="k">try</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="nx">time</span><span class="p">[</span><span class="nx">currentIndex</span><span class="p">].</span><span class="nx">toFixed</span><span class="p">(</span><span class="mf">3</span><span class="p">);</span> +<span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">catch</span><span class="w"> </span><span class="p">(</span><span class="nx">e</span><span class="p">)</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="nx">currentIndex</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span> +<span class="w"> </span><span class="p">}</span> + +<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">data</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span> +<span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="nx">x</span><span class="o">:</span><span class="w"> </span><span class="nx">X</span><span class="p">[</span><span class="mf">0</span><span class="p">].</span><span class="nx">slice</span><span class="p">(</span><span class="nx">tailLength</span><span class="p">,</span><span class="w"> </span><span class="nx">currentIndex</span><span class="p">),</span> +<span class="w"> </span><span class="nx">y</span><span class="o">:</span><span class="w"> </span><span class="nx">Y</span><span class="p">[</span><span class="mf">0</span><span class="p">].</span><span class="nx">slice</span><span class="p">(</span><span class="nx">tailLength</span><span class="p">,</span><span class="w"> </span><span class="nx">currentIndex</span><span class="p">),</span> +<span class="w"> </span><span class="nx">mode</span><span class="o">:</span><span class="w"> </span><span class="s1">'lines+markers'</span><span class="p">,</span> +<span class="w"> </span><span class="nx">marker</span><span class="o">:</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="nx">symbol</span><span class="o">:</span><span class="w"> </span><span class="s1">'star'</span><span class="p">,</span> +<span class="w"> </span><span class="nx">size</span><span class="o">:</span><span class="w"> </span><span class="mf">8</span><span class="p">,</span> +<span class="w"> </span><span class="nx">line</span><span class="o">:</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nx">width</span><span class="o">:</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="p">},</span> +<span class="w"> </span><span class="p">},</span> +<span class="w"> </span><span class="nx">line</span><span class="o">:</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="nx">width</span><span class="o">:</span><span class="w"> </span><span class="mf">2</span><span class="p">,</span> +<span class="w"> </span><span class="p">},</span> +<span class="w"> </span><span class="nx">name</span><span class="o">:</span><span class="w"> </span><span class="s1">''</span><span class="p">,</span> +<span class="w"> </span><span class="p">},</span> +<span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="nx">x</span><span class="o">:</span><span class="w"> </span><span class="nx">X</span><span class="p">[</span><span class="mf">1</span><span class="p">].</span><span class="nx">slice</span><span class="p">(</span><span class="nx">tailLength</span><span class="p">,</span><span class="w"> </span><span class="nx">currentIndex</span><span class="p">),</span> +<span class="w"> </span><span class="nx">y</span><span class="o">:</span><span class="w"> </span><span class="nx">Y</span><span class="p">[</span><span class="mf">1</span><span class="p">].</span><span class="nx">slice</span><span class="p">(</span><span class="nx">tailLength</span><span class="p">,</span><span class="w"> </span><span class="nx">currentIndex</span><span class="p">),</span> +<span class="w"> </span><span class="nx">mode</span><span class="o">:</span><span class="w"> </span><span class="s1">'lines+markers'</span><span class="p">,</span> +<span class="w"> </span><span class="nx">marker</span><span class="o">:</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="nx">symbol</span><span class="o">:</span><span class="w"> </span><span class="s1">'star'</span><span class="p">,</span> +<span class="w"> </span><span class="nx">size</span><span class="o">:</span><span class="w"> </span><span class="mf">8</span><span class="p">,</span> +<span class="w"> </span><span class="nx">line</span><span class="o">:</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nx">width</span><span class="o">:</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="p">},</span> +<span class="w"> </span><span class="p">},</span> +<span class="w"> </span><span class="nx">line</span><span class="o">:</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="nx">width</span><span class="o">:</span><span class="w"> </span><span class="mf">2</span><span class="p">,</span> +<span class="w"> </span><span class="p">},</span> +<span class="w"> </span><span class="nx">name</span><span class="o">:</span><span class="w"> </span><span class="s1">''</span><span class="p">,</span> +<span class="w"> </span><span class="p">},</span> +<span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="nx">x</span><span class="o">:</span><span class="w"> </span><span class="nx">X</span><span class="p">[</span><span class="mf">2</span><span class="p">].</span><span class="nx">slice</span><span class="p">(</span><span class="nx">tailLength</span><span class="p">,</span><span class="w"> </span><span class="nx">currentIndex</span><span class="p">),</span> +<span class="w"> </span><span class="nx">y</span><span class="o">:</span><span class="w"> </span><span class="nx">Y</span><span class="p">[</span><span class="mf">2</span><span class="p">].</span><span class="nx">slice</span><span class="p">(</span><span class="nx">tailLength</span><span class="p">,</span><span class="w"> </span><span class="nx">currentIndex</span><span class="p">),</span> +<span class="w"> </span><span class="nx">mode</span><span class="o">:</span><span class="w"> </span><span class="s1">'lines+markers'</span><span class="p">,</span> +<span class="w"> </span><span class="nx">marker</span><span class="o">:</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="nx">symbol</span><span class="o">:</span><span class="w"> </span><span class="s1">'star'</span><span class="p">,</span> +<span class="w"> </span><span class="nx">size</span><span class="o">:</span><span class="w"> </span><span class="mf">8</span><span class="p">,</span> +<span class="w"> </span><span class="nx">line</span><span class="o">:</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nx">width</span><span class="o">:</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="p">},</span> +<span class="w"> </span><span class="p">},</span> +<span class="w"> </span><span class="nx">line</span><span class="o">:</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="nx">width</span><span class="o">:</span><span class="w"> </span><span class="mf">2</span><span class="p">,</span> +<span class="w"> </span><span class="p">},</span> +<span class="w"> </span><span class="nx">name</span><span class="o">:</span><span class="w"> </span><span class="s1">''</span><span class="p">,</span> +<span class="w"> </span><span class="p">},</span> +<span class="w"> </span><span class="p">];</span> + +<span class="w"> </span><span class="c1">// width: 1000, height: 400</span> +<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">layout</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="nx">title</span><span class="o">:</span><span class="w"> </span><span class="s1">'∞ Three-Body Problem: t = '</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">time</span><span class="p">[</span><span class="nx">currentIndex</span><span class="p">].</span><span class="nx">toFixed</span><span class="p">(</span><span class="mf">3</span><span class="p">),</span> +<span class="w"> </span><span class="nx">xaxis</span><span class="o">:</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="nx">title</span><span class="o">:</span><span class="w"> </span><span class="s1">'x'</span><span class="p">,</span> +<span class="w"> </span><span class="nx">range</span><span class="o">:</span><span class="w"> </span><span class="p">[</span><span class="o">-</span><span class="mf">1.1</span><span class="p">,</span><span class="mf">1.1</span><span class="p">]</span> +<span class="w"> </span><span class="p">},</span> +<span class="w"> </span><span class="nx">yaxis</span><span class="o">:</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="nx">title</span><span class="o">:</span><span class="w"> </span><span class="s1">'y'</span><span class="p">,</span> +<span class="w"> </span><span class="nx">scaleanchor</span><span class="o">:</span><span class="w"> </span><span class="s1">'x'</span><span class="p">,</span> +<span class="w"> </span><span class="nx">scaleratio</span><span class="o">:</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span> +<span class="w"> </span><span class="nx">range</span><span class="o">:</span><span class="w"> </span><span class="p">[</span><span class="o">-</span><span class="mf">0.5</span><span class="p">,</span><span class="mf">0.5</span><span class="p">]</span> +<span class="w"> </span><span class="p">},</span> +<span class="w"> </span><span class="nx">plot_bgcolor</span><span class="o">:</span><span class="w"> </span><span class="s1">'black'</span><span class="p">,</span> +<span class="w"> </span><span class="nx">paper_bgcolor</span><span class="o">:</span><span class="w"> </span><span class="s1">'black'</span><span class="p">,</span> +<span class="w"> </span><span class="nx">font</span><span class="o">:</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="nx">color</span><span class="o">:</span><span class="w"> </span><span class="s1">'white'</span><span class="p">,</span> +<span class="w"> </span><span class="p">},</span> +<span class="w"> </span><span class="p">};</span> + +<span class="w"> </span><span class="k">try</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="nx">Plotly</span><span class="p">.</span><span class="nx">animate</span><span class="p">(</span><span class="s2">"plot"</span><span class="p">,</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="nx">data</span><span class="o">:</span><span class="w"> </span><span class="nx">data</span><span class="p">,</span><span class="w"> </span><span class="nx">layout</span><span class="o">:</span><span class="w"> </span><span class="nx">layout</span> +<span class="w"> </span><span class="p">},</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="nx">staticPlot</span><span class="o">:</span><span class="w"> </span><span class="kc">true</span><span class="p">,</span> +<span class="w"> </span><span class="nx">transition</span><span class="o">:</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="nx">duration</span><span class="o">:</span><span class="w"> </span><span class="mf">0</span><span class="p">,</span> +<span class="w"> </span><span class="p">},</span> +<span class="w"> </span><span class="nx">frame</span><span class="o">:</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="nx">duration</span><span class="o">:</span><span class="w"> </span><span class="mf">0</span><span class="p">,</span> +<span class="w"> </span><span class="nx">redraw</span><span class="o">:</span><span class="w"> </span><span class="kc">false</span><span class="p">,</span> +<span class="w"> </span><span class="p">}</span> +<span class="w"> </span><span class="p">});</span> +<span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">catch</span><span class="w"> </span><span class="p">(</span><span class="nx">err</span><span class="p">)</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="nx">Plotly</span><span class="p">.</span><span class="nx">newPlot</span><span class="p">(</span><span class="s1">'plot'</span><span class="p">,</span><span class="w"> </span><span class="nx">data</span><span class="p">,</span><span class="w"> </span><span class="nx">layout</span><span class="p">);</span> +<span class="w"> </span><span class="p">}</span> + + +<span class="w"> </span><span class="nx">plotIndex</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="nx">delay</span><span class="p">;</span> +<span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">plotClassic</span><span class="o">===</span><span class="kc">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="k">try</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="nx">requestAnimationFrame</span><span class="p">(</span><span class="nx">plotClassicFunc</span><span class="p">);</span> +<span class="w"> </span><span class="p">}</span> +<span class="w"> </span><span class="k">catch</span><span class="w"> </span><span class="p">(</span><span class="nx">err</span><span class="p">)</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="nx">err</span><span class="p">)</span> +<span class="w"> </span><span class="p">}</span> +<span class="w"> </span><span class="p">}</span> + +<span class="w"> </span><span class="p">}</span> +</code></pre> +</div> <h2>"General" N-Body Solver</h2> <h3>Show me the code!</h3> <div class="codehilite"> -<pre><span></span><code><span class="kd">function</span><span class="w"> </span><span class="nx">step</span><span class="p">(</span><span class="nx">coords</span><span class="p">,</span><span class="w"> </span><span class="nx">masses</span><span class="p">,</span><span class="w"> </span><span class="nx">deltaT</span><span class="p">,</span><span class="w"> </span><span class="nx">nBodies</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">3</span><span class="p">,</span><span class="w"> </span><span class="nx">G</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">6.67408313131313e-11</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"></span> -<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">k1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">math</span><span class="p">.</span><span class="nx">multiply</span><span class="p">(</span><span class="nx">deltaT</span><span class="p">,</span><span class="w"> </span><span class="nx">deltaR</span><span class="p">(</span><span class="nx">coords</span><span class="p">,</span><span class="w"> </span><span class="nx">masses</span><span class="p">,</span><span class="w"> </span><span class="nx">nBodies</span><span class="p">,</span><span class="w"> </span><span class="nx">G</span><span class="p">));</span><span class="w"></span> -<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">k2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">math</span><span class="p">.</span><span class="nx">multiply</span><span class="p">(</span><span class="nx">deltaT</span><span class="p">,</span><span class="w"> </span><span class="nx">deltaR</span><span class="p">(</span><span class="nx">math</span><span class="p">.</span><span class="nx">add</span><span class="p">(</span><span class="nx">coords</span><span class="p">,</span><span class="w"> </span><span class="nx">math</span><span class="p">.</span><span class="nx">multiply</span><span class="p">(</span><span class="nx">k1</span><span class="p">,</span><span class="w"> </span><span class="mf">0.5</span><span class="p">)),</span><span class="w"> </span><span class="nx">masses</span><span class="p">,</span><span class="w"> </span><span class="nx">nBodies</span><span class="p">,</span><span class="w"> </span><span class="nx">G</span><span class="p">));</span><span class="w"></span> -<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">k3</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">math</span><span class="p">.</span><span class="nx">multiply</span><span class="p">(</span><span class="nx">deltaT</span><span class="p">,</span><span class="w"> </span><span class="nx">deltaR</span><span class="p">(</span><span class="nx">math</span><span class="p">.</span><span class="nx">add</span><span class="p">(</span><span class="nx">coords</span><span class="p">,</span><span class="w"> </span><span class="nx">math</span><span class="p">.</span><span class="nx">multiply</span><span class="p">(</span><span class="nx">k2</span><span class="p">,</span><span class="w"> </span><span class="mf">0.5</span><span class="p">)),</span><span class="w"> </span><span class="nx">masses</span><span class="p">,</span><span class="w"> </span><span class="nx">nBodies</span><span class="p">,</span><span class="w"> </span><span class="nx">G</span><span class="p">));</span><span class="w"></span> -<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">k4</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">math</span><span class="p">.</span><span class="nx">multiply</span><span class="p">(</span><span class="nx">deltaT</span><span class="p">,</span><span class="w"> </span><span class="nx">deltaR</span><span class="p">(</span><span class="nx">math</span><span class="p">.</span><span class="nx">add</span><span class="p">(</span><span class="nx">coords</span><span class="p">,</span><span class="w"> </span><span class="nx">k3</span><span class="p">),</span><span class="w"> </span><span class="nx">masses</span><span class="p">,</span><span class="w"> </span><span class="nx">nBodies</span><span class="p">,</span><span class="w"> </span><span class="nx">G</span><span class="p">));</span><span class="w"></span> - -<span class="w"> </span><span class="nx">coords</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">math</span><span class="p">.</span><span class="nx">add</span><span class="p">(</span><span class="nx">coords</span><span class="p">,</span><span class="w"> </span><span class="nx">math</span><span class="p">.</span><span class="nx">multiply</span><span class="p">(</span><span class="nx">math</span><span class="p">.</span><span class="nx">add</span><span class="p">(</span><span class="nx">k1</span><span class="p">,</span><span class="w"> </span><span class="nx">math</span><span class="p">.</span><span class="nx">multiply</span><span class="p">(</span><span class="mf">2.0</span><span class="p">,</span><span class="w"> </span><span class="nx">k2</span><span class="p">),</span><span class="w"> </span><span class="nx">math</span><span class="p">.</span><span class="nx">multiply</span><span class="p">(</span><span class="mf">2.0</span><span class="p">,</span><span class="w"> </span><span class="nx">k3</span><span class="p">),</span><span class="w"> </span><span class="nx">k4</span><span class="p">),</span><span class="w"> </span><span class="mf">1</span><span class="o">/</span><span class="mf">6</span><span class="p">));</span><span class="w"></span> - -<span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">coords</span><span class="p">;</span><span class="w"></span> -<span class="p">}</span><span class="w"></span> - -<span class="kd">function</span><span class="w"> </span><span class="nx">detectCollisionsEscape</span><span class="p">(</span><span class="nx">coords</span><span class="p">,</span><span class="w"> </span><span class="nx">deltaT</span><span class="p">,</span><span class="w"> </span><span class="nx">maxSep</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"></span> -<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="p">[</span><span class="nx">x</span><span class="p">,</span><span class="w"> </span><span class="nx">y</span><span class="p">,</span><span class="w"> </span><span class="nx">vx</span><span class="p">,</span><span class="w"> </span><span class="nx">vy</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">coords</span><span class="p">;</span><span class="w"></span> -<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">V</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">vx</span><span class="p">.</span><span class="nx">map</span><span class="p">((</span><span class="nx">v</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">sqrt</span><span class="p">(</span><span class="nx">v</span><span class="w"> </span><span class="o">**</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">vy</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">**</span><span class="w"> </span><span class="mf">2</span><span class="p">));</span><span class="w"></span> -<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">R</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">V</span><span class="p">.</span><span class="nx">map</span><span class="p">(</span><span class="nx">v</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="nx">v</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">deltaT</span><span class="p">);</span><span class="w"></span> -<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">collision</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">false</span><span class="p">,</span><span class="w"> </span><span class="nx">collisionInds</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="nx">escape</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">false</span><span class="p">,</span><span class="w"> </span><span class="nx">escapeInd</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span><span class="w"></span> - -<span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">x</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span><span class="w"> </span><span class="nx">n</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"></span> -<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">rn</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">R</span><span class="p">[</span><span class="nx">n</span><span class="p">],</span><span class="w"> </span><span class="nx">xn</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">x</span><span class="p">[</span><span class="nx">n</span><span class="p">],</span><span class="w"> </span><span class="nx">yn</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">y</span><span class="p">[</span><span class="nx">n</span><span class="p">];</span><span class="w"></span> -<span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">x</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"></span> -<span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"></span> -<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">minSep</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">rn</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">R</span><span class="p">[</span><span class="nx">i</span><span class="p">];</span><span class="w"></span> -<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">sep</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">sqrt</span><span class="p">((</span><span class="nx">xn</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">x</span><span class="p">[</span><span class="nx">i</span><span class="p">])</span><span class="w"> </span><span class="o">**</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="nx">yn</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">y</span><span class="p">[</span><span class="nx">i</span><span class="p">])</span><span class="w"> </span><span class="o">**</span><span class="w"> </span><span class="mf">2</span><span class="p">);</span><span class="w"></span> -<span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">sep</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">minSep</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"></span> -<span class="w"> </span><span class="nx">collision</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">true</span><span class="p">;</span><span class="w"></span> -<span class="w"> </span><span class="nx">collisionInds</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="nx">n</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">];</span><span class="w"></span> -<span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">sep</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="nx">maxSep</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"></span> -<span class="w"> </span><span class="nx">escape</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">true</span><span class="p">;</span><span class="w"></span> -<span class="w"> </span><span class="nx">escapeInd</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"></span> -<span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="p">[</span><span class="nx">collision</span><span class="p">,</span><span class="w"> </span><span class="nx">collisionInds</span><span class="p">,</span><span class="w"> </span><span class="nx">escape</span><span class="p">,</span><span class="w"> </span><span class="nx">escapeInd</span><span class="p">];</span><span class="w"></span> -<span class="w"> </span><span class="p">}</span><span class="w"></span> -<span class="w"> </span><span class="p">}</span><span class="w"></span> -<span class="w"> </span><span class="p">}</span><span class="w"></span> -<span class="w"> </span><span class="p">}</span><span class="w"></span> -<span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="p">[</span><span class="nx">collision</span><span class="p">,</span><span class="w"> </span><span class="nx">collisionInds</span><span class="p">,</span><span class="w"> </span><span class="nx">escape</span><span class="p">,</span><span class="w"> </span><span class="nx">escapeInd</span><span class="p">];</span><span class="w"></span> -<span class="p">}</span><span class="w"></span> - -<span class="kd">function</span><span class="w"> </span><span class="nx">nBodyStep</span><span class="p">(</span><span class="nx">coords</span><span class="p">,</span><span class="w"> </span><span class="nx">masses</span><span class="p">,</span><span class="w"> </span><span class="nx">deltaT</span><span class="p">,</span><span class="w"> </span><span class="nx">maxSep</span><span class="p">,</span><span class="w"> </span><span class="nx">nBodies</span><span class="p">,</span><span class="w"> </span><span class="nx">G</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">6.67408313131313e-11</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// Similar to our step function before, but keeping track of collisions</span><span class="w"></span> -<span class="w"> </span><span class="nx">coords</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">step</span><span class="p">(</span><span class="nx">coords</span><span class="p">,</span><span class="w"> </span><span class="nx">masses</span><span class="p">,</span><span class="w"> </span><span class="nx">deltaT</span><span class="p">,</span><span class="w"> </span><span class="nx">nBodies</span><span class="p">,</span><span class="w"> </span><span class="nx">G</span><span class="p">);</span><span class="w"> </span><span class="c1">// Update the positions as we did before</span><span class="w"></span> -<span class="w"> </span><span class="c1">//console.log(detectCollisionsEscape(coords, deltaT, maxSep));</span><span class="w"></span> -<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="p">[</span><span class="nx">collision</span><span class="p">,</span><span class="w"> </span><span class="nx">collisionInds</span><span class="p">,</span><span class="w"> </span><span class="nx">escape</span><span class="p">,</span><span class="w"> </span><span class="nx">escapeInd</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">detectCollisionsEscape</span><span class="p">(</span><span class="nx">coords</span><span class="p">,</span><span class="w"> </span><span class="nx">deltaT</span><span class="p">,</span><span class="w"> </span><span class="nx">maxSep</span><span class="p">);</span><span class="w"> </span><span class="c1">// Detect collisions/escapes</span><span class="w"></span> - - -<span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">collision</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// Do inelastic collision and delete extra body (2 -> 1)</span><span class="w"></span> -<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="p">[</span><span class="nx">i1</span><span class="p">,</span><span class="w"> </span><span class="nx">i2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">collisionInds</span><span class="p">;</span><span class="w"></span> -<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="p">[</span><span class="nx">x1</span><span class="p">,</span><span class="w"> </span><span class="nx">x2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="nx">coords</span><span class="p">[</span><span class="mf">0</span><span class="p">][</span><span class="nx">i1</span><span class="p">],</span><span class="w"> </span><span class="nx">coords</span><span class="p">[</span><span class="mf">0</span><span class="p">][</span><span class="nx">i2</span><span class="p">]];</span><span class="w"></span> -<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="p">[</span><span class="nx">y1</span><span class="p">,</span><span class="w"> </span><span class="nx">y2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="nx">coords</span><span class="p">[</span><span class="mf">1</span><span class="p">][</span><span class="nx">i1</span><span class="p">],</span><span class="w"> </span><span class="nx">coords</span><span class="p">[</span><span class="mf">1</span><span class="p">][</span><span class="nx">i2</span><span class="p">]];</span><span class="w"></span> -<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="p">[</span><span class="nx">vx1</span><span class="p">,</span><span class="w"> </span><span class="nx">vx2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="nx">coords</span><span class="p">[</span><span class="mf">2</span><span class="p">][</span><span class="nx">i1</span><span class="p">],</span><span class="w"> </span><span class="nx">coords</span><span class="p">[</span><span class="mf">2</span><span class="p">][</span><span class="nx">i2</span><span class="p">]];</span><span class="w"></span> -<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="p">[</span><span class="nx">vy1</span><span class="p">,</span><span class="w"> </span><span class="nx">vy2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="nx">coords</span><span class="p">[</span><span class="mf">3</span><span class="p">][</span><span class="nx">i1</span><span class="p">],</span><span class="w"> </span><span class="nx">coords</span><span class="p">[</span><span class="mf">3</span><span class="p">][</span><span class="nx">i2</span><span class="p">]];</span><span class="w"></span> -<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="p">[</span><span class="nx">px1</span><span class="p">,</span><span class="w"> </span><span class="nx">px2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="nx">masses</span><span class="p">[</span><span class="nx">i1</span><span class="p">]</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">vx1</span><span class="p">,</span><span class="w"> </span><span class="nx">masses</span><span class="p">[</span><span class="nx">i2</span><span class="p">]</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">vx2</span><span class="p">];</span><span class="w"></span> -<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="p">[</span><span class="nx">py1</span><span class="p">,</span><span class="w"> </span><span class="nx">py2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="nx">masses</span><span class="p">[</span><span class="nx">i1</span><span class="p">]</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">vy1</span><span class="p">,</span><span class="w"> </span><span class="nx">masses</span><span class="p">[</span><span class="nx">i2</span><span class="p">]</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">vy2</span><span class="p">];</span><span class="w"></span> -<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">px</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">px1</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">px2</span><span class="p">;</span><span class="w"></span> -<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">py</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">py1</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">py2</span><span class="p">;</span><span class="w"></span> -<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">newM</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">masses</span><span class="p">[</span><span class="nx">i1</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">masses</span><span class="p">[</span><span class="nx">i2</span><span class="p">];</span><span class="w"></span> -<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">vfx</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">px</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="nx">newM</span><span class="p">;</span><span class="w"></span> -<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">vfy</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">py</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="nx">newM</span><span class="p">;</span><span class="w"></span> -<span class="w"> </span><span class="nx">coords</span><span class="p">[</span><span class="mf">0</span><span class="p">][</span><span class="nx">i1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="nx">x1</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">masses</span><span class="p">[</span><span class="nx">i1</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">x2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">masses</span><span class="p">[</span><span class="nx">i2</span><span class="p">])</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="p">(</span><span class="nx">masses</span><span class="p">[</span><span class="nx">i1</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">masses</span><span class="p">[</span><span class="nx">i2</span><span class="p">]);</span><span class="w"> </span><span class="c1">// Center of mass</span><span class="w"></span> -<span class="w"> </span><span class="nx">coords</span><span class="p">[</span><span class="mf">1</span><span class="p">][</span><span class="nx">i1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="nx">y1</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">masses</span><span class="p">[</span><span class="nx">i1</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">y2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">masses</span><span class="p">[</span><span class="nx">i2</span><span class="p">])</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="p">(</span><span class="nx">masses</span><span class="p">[</span><span class="nx">i1</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">masses</span><span class="p">[</span><span class="nx">i2</span><span class="p">]);</span><span class="w"></span> -<span class="w"> </span><span class="nx">coords</span><span class="p">[</span><span class="mf">2</span><span class="p">][</span><span class="nx">i1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">vfx</span><span class="p">;</span><span class="w"></span> -<span class="w"> </span><span class="nx">coords</span><span class="p">[</span><span class="mf">3</span><span class="p">][</span><span class="nx">i1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">vfy</span><span class="p">;</span><span class="w"></span> -<span class="w"> </span><span class="nx">coords</span><span class="p">[</span><span class="mf">0</span><span class="p">].</span><span class="nx">splice</span><span class="p">(</span><span class="nx">i2</span><span class="p">,</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span><span class="w"></span> -<span class="w"> </span><span class="nx">coords</span><span class="p">[</span><span class="mf">1</span><span class="p">].</span><span class="nx">splice</span><span class="p">(</span><span class="nx">i2</span><span class="p">,</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span><span class="w"></span> -<span class="w"> </span><span class="nx">coords</span><span class="p">[</span><span class="mf">2</span><span class="p">].</span><span class="nx">splice</span><span class="p">(</span><span class="nx">i2</span><span class="p">,</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span><span class="w"></span> -<span class="w"> </span><span class="nx">coords</span><span class="p">[</span><span class="mf">3</span><span class="p">].</span><span class="nx">splice</span><span class="p">(</span><span class="nx">i2</span><span class="p">,</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span><span class="w"></span> -<span class="w"> </span><span class="nx">masses</span><span class="p">[</span><span class="nx">i1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">newM</span><span class="p">;</span><span class="w"></span> -<span class="w"> </span><span class="nx">masses</span><span class="p">.</span><span class="nx">splice</span><span class="p">(</span><span class="nx">i2</span><span class="p">,</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span><span class="w"></span> -<span class="w"> </span><span class="nx">nBodies</span><span class="o">--</span><span class="p">;</span><span class="w"></span> -<span class="w"> </span><span class="p">}</span><span class="w"></span> -<span class="w"> </span><span class="c1">// Could also implement condition for escape where we stop calculating forces but I'm too lazy for now</span><span class="w"></span> -<span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="p">[</span><span class="nx">coords</span><span class="p">,</span><span class="w"> </span><span class="nx">masses</span><span class="p">,</span><span class="w"> </span><span class="nx">nBodies</span><span class="p">,</span><span class="w"> </span><span class="nx">collision</span><span class="p">,</span><span class="w"> </span><span class="nx">collisionInds</span><span class="p">,</span><span class="w"> </span><span class="nx">escape</span><span class="p">,</span><span class="w"> </span><span class="nx">escapeInd</span><span class="p">];</span><span class="w"></span> -<span class="p">}</span><span class="w"></span> - -<span class="kd">function</span><span class="w"> </span><span class="nx">uniform</span><span class="p">(</span><span class="nx">min</span><span class="p">,</span><span class="w"> </span><span class="nx">max</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"></span> -<span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">random</span><span class="p">()</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="nx">max</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">min</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">min</span><span class="p">;</span><span class="w"></span> -<span class="p">}</span><span class="w"></span> - -<span class="kd">function</span><span class="w"> </span><span class="nx">deepCopyCoordsArray</span><span class="p">(</span><span class="nx">arr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"></span> -<span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">arr</span><span class="p">.</span><span class="nx">map</span><span class="p">(</span><span class="nx">innerArr</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="nx">innerArr</span><span class="p">.</span><span class="nx">slice</span><span class="p">());</span><span class="w"></span> -<span class="p">}</span><span class="w"></span> - -<span class="kd">function</span><span class="w"> </span><span class="nx">genNBodyResults</span><span class="p">(</span><span class="nx">nBodies</span><span class="p">,</span><span class="w"> </span><span class="nx">tStop</span><span class="p">,</span><span class="w"> </span><span class="nx">nTPts</span><span class="p">,</span><span class="w"> </span><span class="nx">nBodiesStop</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">10</span><span class="p">,</span><span class="w"> </span><span class="nx">G</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">6.67408313131313e-11</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"></span> - -<span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nx">btn</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">document</span><span class="p">.</span><span class="nx">getElementById</span><span class="p">(</span><span class="s2">"startSim3"</span><span class="p">);</span><span class="w"></span> -<span class="w"> </span><span class="c1">// Set button text to Solving</span><span class="w"></span> -<span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nx">prevText</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">btn</span><span class="p">.</span><span class="nx">innerHTML</span><span class="p">;</span><span class="w"></span> -<span class="w"> </span><span class="nx">btn</span><span class="p">.</span><span class="nx">innerHTML</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s2">"Solving..."</span><span class="p">;</span><span class="w"></span> - -<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">coords</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="nb">Array</span><span class="p">(</span><span class="nx">nBodies</span><span class="p">).</span><span class="nx">fill</span><span class="p">(</span><span class="mf">0</span><span class="p">),</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">nBodies</span><span class="p">).</span><span class="nx">fill</span><span class="p">(</span><span class="mf">0</span><span class="p">),</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">nBodies</span><span class="p">).</span><span class="nx">fill</span><span class="p">(</span><span class="mf">0</span><span class="p">),</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">nBodies</span><span class="p">).</span><span class="nx">fill</span><span class="p">(</span><span class="mf">0</span><span class="p">)];</span><span class="w"></span> -<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">Mstar</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">2e30</span><span class="p">;</span><span class="w"></span> -<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">Mp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">Mstar</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">1e4</span><span class="p">;</span><span class="w"></span> - -<span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">nBodies</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// Initialize coordinates on ~Keplerian orbits</span><span class="w"></span> -<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">accept</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">false</span><span class="p">;</span><span class="w"></span> -<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span><span class="w"></span> -<span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="nx">accept</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// Prevent a particle from spawning within 0.2 AU too close to "star"</span><span class="w"></span> -<span class="w"> </span><span class="nx">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">random</span><span class="p">()</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mf">1.5e11</span><span class="p">;</span><span class="w"> </span><span class="c1">// Say radius of 2 AU</span><span class="w"></span> -<span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">r</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">1.5e11</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="mf">0.2</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"></span> -<span class="w"> </span><span class="nx">accept</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">true</span><span class="p">;</span><span class="w"></span> -<span class="w"> </span><span class="p">}</span><span class="w"></span> -<span class="w"> </span><span class="p">}</span><span class="w"></span> -<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">theta</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">uniform</span><span class="p">(</span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">PI</span><span class="p">);</span><span class="w"></span> -<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">x</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">r</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">cos</span><span class="p">(</span><span class="nx">theta</span><span class="p">);</span><span class="w"></span> -<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">y</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">r</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">sin</span><span class="p">(</span><span class="nx">theta</span><span class="p">);</span><span class="w"></span> -<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">v</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">sqrt</span><span class="p">(</span><span class="nx">G</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">Mstar</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="nx">r</span><span class="p">);</span><span class="w"></span> -<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">perturbedV</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">v</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">v</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">1000</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">uniform</span><span class="p">(</span><span class="o">-</span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span><span class="w"> </span><span class="c1">// Perturb the velocities ever so slightly</span><span class="w"></span> -<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">vTheta</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">atan2</span><span class="p">(</span><span class="nx">y</span><span class="p">,</span><span class="w"> </span><span class="nx">x</span><span class="p">);</span><span class="w"></span> -<span class="w"> </span><span class="nx">coords</span><span class="p">[</span><span class="mf">0</span><span class="p">][</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">x</span><span class="p">;</span><span class="w"></span> -<span class="w"> </span><span class="nx">coords</span><span class="p">[</span><span class="mf">1</span><span class="p">][</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">y</span><span class="p">;</span><span class="w"></span> -<span class="w"> </span><span class="nx">coords</span><span class="p">[</span><span class="mf">2</span><span class="p">][</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">-</span><span class="nx">perturbedV</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">sin</span><span class="p">(</span><span class="nx">vTheta</span><span class="p">);</span><span class="w"></span> -<span class="w"> </span><span class="nx">coords</span><span class="p">[</span><span class="mf">3</span><span class="p">][</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">perturbedV</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">cos</span><span class="p">(</span><span class="nx">vTheta</span><span class="p">);</span><span class="w"></span> -<span class="w"> </span><span class="p">}</span><span class="w"></span> - -<span class="w"> </span><span class="c1">//console.log('Initial coords:', coords);</span><span class="w"></span> - - -<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">masses</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">nBodies</span><span class="p">).</span><span class="nx">fill</span><span class="p">(</span><span class="nx">Mp</span><span class="p">);</span><span class="w"> </span><span class="c1">// Initialize masses</span><span class="w"></span> -<span class="w"> </span><span class="nx">masses</span><span class="p">[</span><span class="mf">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">Mstar</span><span class="p">;</span><span class="w"> </span><span class="c1">// Make index one special as the central star</span><span class="w"></span> -<span class="w"> </span><span class="nx">coords</span><span class="p">[</span><span class="mf">0</span><span class="p">][</span><span class="mf">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"></span> -<span class="w"> </span><span class="nx">coords</span><span class="p">[</span><span class="mf">1</span><span class="p">][</span><span class="mf">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"></span> -<span class="w"> </span><span class="nx">coords</span><span class="p">[</span><span class="mf">2</span><span class="p">][</span><span class="mf">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"></span> -<span class="w"> </span><span class="nx">coords</span><span class="p">[</span><span class="mf">3</span><span class="p">][</span><span class="mf">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// Initialize central star at origin with no velocity</span><span class="w"></span> -<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">yearSec</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">365</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mf">24</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mf">3600</span><span class="p">;</span><span class="w"></span> -<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">time</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">.</span><span class="kr">from</span><span class="p">({</span><span class="w"> </span><span class="nx">length</span><span class="o">:</span><span class="w"> </span><span class="nx">nTPts</span><span class="w"> </span><span class="p">},</span><span class="w"> </span><span class="p">(</span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">tStop</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="p">(</span><span class="nx">nTPts</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">yearSec</span><span class="p">);</span><span class="w"> </span><span class="c1">// Years -> s</span><span class="w"></span> -<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">t</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">time</span><span class="p">[</span><span class="mf">0</span><span class="p">];</span><span class="w"></span> -<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">deltaT</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">time</span><span class="p">[</span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">time</span><span class="p">[</span><span class="mf">0</span><span class="p">];</span><span class="w"></span> -<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">tInd</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"></span> -<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">coordsRecord</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="nx">deepCopyCoordsArray</span><span class="p">(</span><span class="nx">coords</span><span class="p">)];</span><span class="w"></span> -<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">massRecord</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="nx">masses</span><span class="p">.</span><span class="nx">slice</span><span class="p">()];</span><span class="w"> </span><span class="c1">// Initialize records with initial conditions</span><span class="w"></span> - - -<span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">tInd</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">nTPts</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="nx">nBodies</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="nx">nBodiesStop</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"></span> -<span class="w"> </span><span class="c1">//console.log('Initial coords:', coords);</span><span class="w"></span> -<span class="w"> </span><span class="p">[</span><span class="nx">coords</span><span class="p">,</span><span class="w"> </span><span class="nx">masses</span><span class="p">,</span><span class="w"> </span><span class="nx">nBodies</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nBodyStep</span><span class="p">(</span><span class="nx">coords</span><span class="p">,</span><span class="w"> </span><span class="nx">masses</span><span class="p">,</span><span class="w"> </span><span class="nx">deltaT</span><span class="p">,</span><span class="w"> </span><span class="mf">10</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mf">1.5e11</span><span class="p">,</span><span class="w"> </span><span class="nx">nBodies</span><span class="p">,</span><span class="w"> </span><span class="nx">G</span><span class="p">);</span><span class="w"> </span><span class="c1">// Update</span><span class="w"></span> -<span class="w"> </span><span class="nx">coordsRecord</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">deepCopyCoordsArray</span><span class="p">(</span><span class="nx">coords</span><span class="p">));</span><span class="w"></span> -<span class="w"> </span><span class="nx">massRecord</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">masses</span><span class="p">.</span><span class="nx">slice</span><span class="p">());</span><span class="w"> </span><span class="c1">// Add to records</span><span class="w"></span> -<span class="w"> </span><span class="nx">tInd</span><span class="o">++</span><span class="p">;</span><span class="w"></span> -<span class="w"> </span><span class="nx">t</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">time</span><span class="p">[</span><span class="nx">tInd</span><span class="p">];</span><span class="w"></span> -<span class="w"> </span><span class="c1">//console.log(`currently at t = ${(t / yearSec).toFixed(2)} years\r`);</span><span class="w"></span> -<span class="w"> </span><span class="p">}</span><span class="w"></span> -<span class="w"> </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="sb">`final time = </span><span class="si">${</span><span class="nx">time</span><span class="p">[</span><span class="nx">tInd</span><span class="p">]</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="nx">yearSec</span><span class="si">}</span><span class="sb"> years with </span><span class="si">${</span><span class="nx">nBodies</span><span class="si">}</span><span class="sb"> bodies remaining`</span><span class="p">);</span><span class="w"></span> - -<span class="w"> </span><span class="c1">// Set button text to Start Simulation</span><span class="w"></span> -<span class="w"> </span><span class="nx">btn</span><span class="p">.</span><span class="nx">innerHTML</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">prevText</span><span class="p">;</span><span class="w"></span> - -<span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="p">[</span><span class="nx">coordsRecord</span><span class="p">,</span><span class="w"> </span><span class="nx">massRecord</span><span class="p">,</span><span class="w"> </span><span class="nx">time</span><span class="p">.</span><span class="nx">slice</span><span class="p">(</span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="nx">tInd</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">)];</span><span class="w"></span> -<span class="p">}</span><span class="w"></span> - - -<span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="p">[</span><span class="nx">coordsRecordR</span><span class="p">,</span><span class="w"> </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">tR</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">genNBodyResults</span><span class="p">(</span><span class="mf">256</span><span class="p">,</span><span class="mf">1</span><span class="p">,</span><span class="mf">1001</span><span class="p">);</span><span class="w"></span> -<span class="w"> </span><span class="c1">//console.log(coordsRecordR);</span><span class="w"></span> -<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">yearSec</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">365</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mf">24</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mf">3600</span><span class="p">;</span><span class="w"></span> - -<span class="w"> </span><span class="kd">function</span><span class="w"> </span><span class="nx">createFrame</span><span class="p">(</span><span class="nx">coordsR</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"></span> -<span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="nx">coordsR</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="o">!</span><span class="nx">coordsR</span><span class="p">[</span><span class="mf">0</span><span class="p">]</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="o">!</span><span class="nx">coordsR</span><span class="p">[</span><span class="mf">1</span><span class="p">])</span><span class="w"> </span><span class="p">{</span><span class="w"></span> -<span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="p">[];</span><span class="w"></span> -<span class="w"> </span><span class="p">}</span><span class="w"></span> - -<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">traceCentralStar</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="w"></span> -<span class="w"> </span><span class="nx">x</span><span class="o">:</span><span class="w"> </span><span class="p">[</span><span class="nx">coordsR</span><span class="p">[</span><span class="mf">0</span><span class="p">][</span><span class="mf">0</span><span class="p">]</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">1.5e11</span><span class="p">],</span><span class="w"></span> -<span class="w"> </span><span class="nx">y</span><span class="o">:</span><span class="w"> </span><span class="p">[</span><span class="nx">coordsR</span><span class="p">[</span><span class="mf">1</span><span class="p">][</span><span class="mf">0</span><span class="p">]</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">1.5e11</span><span class="p">],</span><span class="w"></span> -<span class="w"> </span><span class="nx">mode</span><span class="o">:</span><span class="w"> </span><span class="s1">'markers'</span><span class="p">,</span><span class="w"></span> -<span class="w"> </span><span class="nx">type</span><span class="o">:</span><span class="w"> </span><span class="s1">'scatter'</span><span class="p">,</span><span class="w"></span> -<span class="w"> </span><span class="nx">name</span><span class="o">:</span><span class="w"> </span><span class="s1">'Central star'</span><span class="p">,</span><span class="w"></span> -<span class="w"> </span><span class="nx">marker</span><span class="o">:</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nx">color</span><span class="o">:</span><span class="w"> </span><span class="s1">'gold'</span><span class="p">,</span><span class="w"> </span><span class="nx">symbol</span><span class="o">:</span><span class="w"> </span><span class="s1">'star'</span><span class="p">,</span><span class="w"> </span><span class="nx">size</span><span class="o">:</span><span class="w"> </span><span class="mf">10</span><span class="w"> </span><span class="p">},</span><span class="w"></span> -<span class="w"> </span><span class="p">};</span><span class="w"></span> - -<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">xCoords</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">coordsR</span><span class="p">[</span><span class="mf">0</span><span class="p">].</span><span class="nx">slice</span><span class="p">(</span><span class="mf">1</span><span class="p">).</span><span class="nx">map</span><span class="p">(</span><span class="nx">x</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="nx">x</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">1.5e11</span><span class="p">);</span><span class="w"></span> -<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">yCoords</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">coordsR</span><span class="p">[</span><span class="mf">1</span><span class="p">].</span><span class="nx">slice</span><span class="p">(</span><span class="mf">1</span><span class="p">).</span><span class="nx">map</span><span class="p">(</span><span class="nx">y</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="nx">y</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">1.5e11</span><span class="p">);</span><span class="w"></span> - -<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">traceOtherBodies</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="w"></span> -<span class="w"> </span><span class="nx">x</span><span class="o">:</span><span class="w"> </span><span class="nx">xCoords</span><span class="p">,</span><span class="w"></span> -<span class="w"> </span><span class="nx">y</span><span class="o">:</span><span class="w"> </span><span class="nx">yCoords</span><span class="p">,</span><span class="w"></span> -<span class="w"> </span><span class="nx">mode</span><span class="o">:</span><span class="w"> </span><span class="s1">'markers'</span><span class="p">,</span><span class="w"></span> -<span class="w"> </span><span class="nx">type</span><span class="o">:</span><span class="w"> </span><span class="s1">'scatter'</span><span class="p">,</span><span class="w"></span> -<span class="w"> </span><span class="nx">name</span><span class="o">:</span><span class="w"> </span><span class="s1">''</span><span class="p">,</span><span class="w"></span> -<span class="w"> </span><span class="nx">marker</span><span class="o">:</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nx">color</span><span class="o">:</span><span class="w"> </span><span class="s1">'dodgerblue'</span><span class="p">,</span><span class="w"> </span><span class="nx">symbol</span><span class="o">:</span><span class="w"> </span><span class="s1">'circle'</span><span class="p">,</span><span class="w"> </span><span class="nx">size</span><span class="o">:</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="p">},</span><span class="w"></span> -<span class="w"> </span><span class="p">};</span><span class="w"></span> - -<span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="p">[</span><span class="nx">traceCentralStar</span><span class="p">,</span><span class="w"> </span><span class="nx">traceOtherBodies</span><span class="p">];</span><span class="w"></span> -<span class="w"> </span><span class="p">}</span><span class="w"></span> - - -<span class="w"> </span><span class="kd">function</span><span class="w"> </span><span class="nx">createLayout</span><span class="p">(</span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"></span> -<span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="p">{</span><span class="w"></span> -<span class="w"> </span><span class="nx">title</span><span class="o">:</span><span class="w"> </span><span class="p">{</span><span class="w"></span> -<span class="w"> </span><span class="nx">text</span><span class="o">:</span><span class="w"> </span><span class="sb">`N-Body Problem: t = </span><span class="si">${</span><span class="nb">Number</span><span class="p">(</span><span class="nx">t</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="nx">yearSec</span><span class="p">).</span><span class="nx">toFixed</span><span class="p">(</span><span class="mf">3</span><span class="p">)</span><span class="si">}</span><span class="sb"> years`</span><span class="p">,</span><span class="w"></span> -<span class="w"> </span><span class="nx">x</span><span class="o">:</span><span class="w"> </span><span class="mf">0.03</span><span class="p">,</span><span class="w"></span> -<span class="w"> </span><span class="nx">y</span><span class="o">:</span><span class="w"> </span><span class="mf">0.97</span><span class="p">,</span><span class="w"></span> -<span class="w"> </span><span class="nx">xanchor</span><span class="o">:</span><span class="w"> </span><span class="s1">'left'</span><span class="p">,</span><span class="w"></span> -<span class="w"> </span><span class="nx">yanchor</span><span class="o">:</span><span class="w"> </span><span class="s1">'top'</span><span class="p">,</span><span class="w"></span> -<span class="w"> </span><span class="nx">font</span><span class="o">:</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nx">size</span><span class="o">:</span><span class="w"> </span><span class="mf">14</span><span class="w"> </span><span class="p">},</span><span class="w"></span> -<span class="w"> </span><span class="p">},</span><span class="w"></span> -<span class="w"> </span><span class="nx">xaxis</span><span class="o">:</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nx">title</span><span class="o">:</span><span class="w"> </span><span class="s1">'x [AU]'</span><span class="p">,</span><span class="w"> </span><span class="nx">range</span><span class="o">:</span><span class="w"> </span><span class="p">[</span><span class="o">-</span><span class="mf">2.1</span><span class="p">,</span><span class="w"> </span><span class="mf">2.1</span><span class="p">]</span><span class="w"> </span><span class="p">},</span><span class="w"></span> -<span class="w"> </span><span class="nx">yaxis</span><span class="o">:</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nx">title</span><span class="o">:</span><span class="w"> </span><span class="s1">'y [AU]'</span><span class="p">,</span><span class="w"> </span><span class="nx">range</span><span class="o">:</span><span class="w"> </span><span class="p">[</span><span class="o">-</span><span class="mf">2.1</span><span class="p">,</span><span class="w"> </span><span class="mf">2.1</span><span class="p">],</span><span class="w"> </span><span class="nx">scaleanchor</span><span class="o">:</span><span class="w"> </span><span class="s1">'x'</span><span class="p">,</span><span class="w"> </span><span class="nx">scaleratio</span><span class="o">:</span><span class="w"> </span><span class="mf">1</span><span class="w"> </span><span class="p">},</span><span class="w"></span> -<span class="w"> </span><span class="nx">showlegend</span><span class="o">:</span><span class="w"> </span><span class="kc">false</span><span class="p">,</span><span class="w"></span> -<span class="w"> </span><span class="nx">margin</span><span class="o">:</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nx">l</span><span class="o">:</span><span class="w"> </span><span class="mf">60</span><span class="p">,</span><span class="w"> </span><span class="nx">r</span><span class="o">:</span><span class="w"> </span><span class="mf">40</span><span class="p">,</span><span class="w"> </span><span class="nx">t</span><span class="o">:</span><span class="w"> </span><span class="mf">40</span><span class="p">,</span><span class="w"> </span><span class="nx">b</span><span class="o">:</span><span class="w"> </span><span class="mf">40</span><span class="w"> </span><span class="p">},</span><span class="w"></span> -<span class="w"> </span><span class="nx">width</span><span class="o">:</span><span class="w"> </span><span class="mf">800</span><span class="p">,</span><span class="w"></span> -<span class="w"> </span><span class="nx">height</span><span class="o">:</span><span class="w"> </span><span class="mf">800</span><span class="p">,</span><span class="w"></span> -<span class="w"> </span><span class="nx">plot_bgcolor</span><span class="o">:</span><span class="w"> </span><span class="s1">'black'</span><span class="p">,</span><span class="w"></span> -<span class="w"> </span><span class="p">};</span><span class="w"></span> -<span class="p">}</span><span class="w"></span> - -<span class="w"> </span><span class="kd">function</span><span class="w"> </span><span class="nx">animateNBodyProblem</span><span class="p">()</span><span class="w"> </span><span class="p">{</span><span class="w"></span> -<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">nFrames</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">tR</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span><span class="w"></span> - -<span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">nFrames</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"></span> -<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">frameData</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">createFrame</span><span class="p">(</span><span class="nx">coordsRecordR</span><span class="p">[</span><span class="nx">i</span><span class="p">]);</span><span class="w"></span> -<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">layout</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">createLayout</span><span class="p">(</span><span class="nx">i</span><span class="p">);</span><span class="w"></span> -<span class="w"> </span><span class="c1">//Plotly.newPlot(plotDiv, frameData, layout);</span><span class="w"></span> -<span class="w"> </span><span class="k">try</span><span class="w"> </span><span class="p">{</span><span class="w"></span> -<span class="w"> </span><span class="nx">Plotly</span><span class="p">.</span><span class="nx">animate</span><span class="p">(</span><span class="s2">"plot"</span><span class="p">,</span><span class="w"> </span><span class="p">{</span><span class="w"></span> -<span class="w"> </span><span class="nx">data</span><span class="o">:</span><span class="w"> </span><span class="nx">frameData</span><span class="p">,</span><span class="w"> </span><span class="nx">layout</span><span class="o">:</span><span class="w"> </span><span class="nx">layout</span><span class="w"></span> -<span class="w"> </span><span class="p">},</span><span class="w"> </span><span class="p">{</span><span class="w"></span> -<span class="w"> </span><span class="nx">staticPlot</span><span class="o">:</span><span class="w"> </span><span class="kc">true</span><span class="p">,</span><span class="w"></span> -<span class="w"> </span><span class="nx">transition</span><span class="o">:</span><span class="w"> </span><span class="p">{</span><span class="w"></span> -<span class="w"> </span><span class="nx">duration</span><span class="o">:</span><span class="w"> </span><span class="mf">0</span><span class="p">,</span><span class="w"></span> -<span class="w"> </span><span class="p">},</span><span class="w"></span> -<span class="w"> </span><span class="nx">frame</span><span class="o">:</span><span class="w"> </span><span class="p">{</span><span class="w"></span> -<span class="w"> </span><span class="nx">duration</span><span class="o">:</span><span class="w"> </span><span class="mf">0</span><span class="p">,</span><span class="w"></span> -<span class="w"> </span><span class="nx">redraw</span><span class="o">:</span><span class="w"> </span><span class="kc">false</span><span class="p">,</span><span class="w"></span> -<span class="w"> </span><span class="p">}</span><span class="w"></span> -<span class="w"> </span><span class="p">});</span><span class="w"></span> -<span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">catch</span><span class="w"> </span><span class="p">(</span><span class="nx">err</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"></span> -<span class="w"> </span><span class="nx">Plotly</span><span class="p">.</span><span class="nx">newPlot</span><span class="p">(</span><span class="s1">'plot'</span><span class="p">,</span><span class="w"> </span><span class="nx">frameData</span><span class="p">,</span><span class="w"> </span><span class="nx">layout</span><span class="p">);</span><span class="w"></span> -<span class="w"> </span><span class="p">}</span><span class="w"></span> -<span class="w"> </span><span class="p">}</span><span class="w"></span> -<span class="p">}</span><span class="w"></span> - -<span class="nx">animateNBodyProblem</span><span class="p">();</span><span class="w"></span> +<pre><span></span><code><span class="kd">function</span><span class="w"> </span><span class="nx">step</span><span class="p">(</span><span class="nx">coords</span><span class="p">,</span><span class="w"> </span><span class="nx">masses</span><span class="p">,</span><span class="w"> </span><span class="nx">deltaT</span><span class="p">,</span><span class="w"> </span><span class="nx">nBodies</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">3</span><span class="p">,</span><span class="w"> </span><span class="nx">G</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">6.67408313131313e-11</span><span class="p">)</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">k1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">math</span><span class="p">.</span><span class="nx">multiply</span><span class="p">(</span><span class="nx">deltaT</span><span class="p">,</span><span class="w"> </span><span class="nx">deltaR</span><span class="p">(</span><span class="nx">coords</span><span class="p">,</span><span class="w"> </span><span class="nx">masses</span><span class="p">,</span><span class="w"> </span><span class="nx">nBodies</span><span class="p">,</span><span class="w"> </span><span class="nx">G</span><span class="p">));</span> +<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">k2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">math</span><span class="p">.</span><span class="nx">multiply</span><span class="p">(</span><span class="nx">deltaT</span><span class="p">,</span><span class="w"> </span><span class="nx">deltaR</span><span class="p">(</span><span class="nx">math</span><span class="p">.</span><span class="nx">add</span><span class="p">(</span><span class="nx">coords</span><span class="p">,</span><span class="w"> </span><span class="nx">math</span><span class="p">.</span><span class="nx">multiply</span><span class="p">(</span><span class="nx">k1</span><span class="p">,</span><span class="w"> </span><span class="mf">0.5</span><span class="p">)),</span><span class="w"> </span><span class="nx">masses</span><span class="p">,</span><span class="w"> </span><span class="nx">nBodies</span><span class="p">,</span><span class="w"> </span><span class="nx">G</span><span class="p">));</span> +<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">k3</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">math</span><span class="p">.</span><span class="nx">multiply</span><span class="p">(</span><span class="nx">deltaT</span><span class="p">,</span><span class="w"> </span><span class="nx">deltaR</span><span class="p">(</span><span class="nx">math</span><span class="p">.</span><span class="nx">add</span><span class="p">(</span><span class="nx">coords</span><span class="p">,</span><span class="w"> </span><span class="nx">math</span><span class="p">.</span><span class="nx">multiply</span><span class="p">(</span><span class="nx">k2</span><span class="p">,</span><span class="w"> </span><span class="mf">0.5</span><span class="p">)),</span><span class="w"> </span><span class="nx">masses</span><span class="p">,</span><span class="w"> </span><span class="nx">nBodies</span><span class="p">,</span><span class="w"> </span><span class="nx">G</span><span class="p">));</span> +<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">k4</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">math</span><span class="p">.</span><span class="nx">multiply</span><span class="p">(</span><span class="nx">deltaT</span><span class="p">,</span><span class="w"> </span><span class="nx">deltaR</span><span class="p">(</span><span class="nx">math</span><span class="p">.</span><span class="nx">add</span><span class="p">(</span><span class="nx">coords</span><span class="p">,</span><span class="w"> </span><span class="nx">k3</span><span class="p">),</span><span class="w"> </span><span class="nx">masses</span><span class="p">,</span><span class="w"> </span><span class="nx">nBodies</span><span class="p">,</span><span class="w"> </span><span class="nx">G</span><span class="p">));</span> + +<span class="w"> </span><span class="nx">coords</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">math</span><span class="p">.</span><span class="nx">add</span><span class="p">(</span><span class="nx">coords</span><span class="p">,</span><span class="w"> </span><span class="nx">math</span><span class="p">.</span><span class="nx">multiply</span><span class="p">(</span><span class="nx">math</span><span class="p">.</span><span class="nx">add</span><span class="p">(</span><span class="nx">k1</span><span class="p">,</span><span class="w"> </span><span class="nx">math</span><span class="p">.</span><span class="nx">multiply</span><span class="p">(</span><span class="mf">2.0</span><span class="p">,</span><span class="w"> </span><span class="nx">k2</span><span class="p">),</span><span class="w"> </span><span class="nx">math</span><span class="p">.</span><span class="nx">multiply</span><span class="p">(</span><span class="mf">2.0</span><span class="p">,</span><span class="w"> </span><span class="nx">k3</span><span class="p">),</span><span class="w"> </span><span class="nx">k4</span><span class="p">),</span><span class="w"> </span><span class="mf">1</span><span class="o">/</span><span class="mf">6</span><span class="p">));</span> + +<span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">coords</span><span class="p">;</span> +<span class="p">}</span> + +<span class="kd">function</span><span class="w"> </span><span class="nx">detectCollisionsEscape</span><span class="p">(</span><span class="nx">coords</span><span class="p">,</span><span class="w"> </span><span class="nx">deltaT</span><span class="p">,</span><span class="w"> </span><span class="nx">maxSep</span><span class="p">)</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="p">[</span><span class="nx">x</span><span class="p">,</span><span class="w"> </span><span class="nx">y</span><span class="p">,</span><span class="w"> </span><span class="nx">vx</span><span class="p">,</span><span class="w"> </span><span class="nx">vy</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">coords</span><span class="p">;</span> +<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">V</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">vx</span><span class="p">.</span><span class="nx">map</span><span class="p">((</span><span class="nx">v</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">sqrt</span><span class="p">(</span><span class="nx">v</span><span class="w"> </span><span class="o">**</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">vy</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">**</span><span class="w"> </span><span class="mf">2</span><span class="p">));</span> +<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">R</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">V</span><span class="p">.</span><span class="nx">map</span><span class="p">(</span><span class="nx">v</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="nx">v</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">deltaT</span><span class="p">);</span> +<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">collision</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">false</span><span class="p">,</span><span class="w"> </span><span class="nx">collisionInds</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="nx">escape</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">false</span><span class="p">,</span><span class="w"> </span><span class="nx">escapeInd</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span> + +<span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">x</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span><span class="w"> </span><span class="nx">n</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">rn</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">R</span><span class="p">[</span><span class="nx">n</span><span class="p">],</span><span class="w"> </span><span class="nx">xn</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">x</span><span class="p">[</span><span class="nx">n</span><span class="p">],</span><span class="w"> </span><span class="nx">yn</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">y</span><span class="p">[</span><span class="nx">n</span><span class="p">];</span> +<span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">x</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">minSep</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">rn</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">R</span><span class="p">[</span><span class="nx">i</span><span class="p">];</span> +<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">sep</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">sqrt</span><span class="p">((</span><span class="nx">xn</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">x</span><span class="p">[</span><span class="nx">i</span><span class="p">])</span><span class="w"> </span><span class="o">**</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="nx">yn</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">y</span><span class="p">[</span><span class="nx">i</span><span class="p">])</span><span class="w"> </span><span class="o">**</span><span class="w"> </span><span class="mf">2</span><span class="p">);</span> +<span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">sep</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">minSep</span><span class="p">)</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="nx">collision</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">true</span><span class="p">;</span> +<span class="w"> </span><span class="nx">collisionInds</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="nx">n</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">];</span> +<span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">sep</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="nx">maxSep</span><span class="p">)</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="nx">escape</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">true</span><span class="p">;</span> +<span class="w"> </span><span class="nx">escapeInd</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span> +<span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="p">[</span><span class="nx">collision</span><span class="p">,</span><span class="w"> </span><span class="nx">collisionInds</span><span class="p">,</span><span class="w"> </span><span class="nx">escape</span><span class="p">,</span><span class="w"> </span><span class="nx">escapeInd</span><span class="p">];</span> +<span class="w"> </span><span class="p">}</span> +<span class="w"> </span><span class="p">}</span> +<span class="w"> </span><span class="p">}</span> +<span class="w"> </span><span class="p">}</span> +<span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="p">[</span><span class="nx">collision</span><span class="p">,</span><span class="w"> </span><span class="nx">collisionInds</span><span class="p">,</span><span class="w"> </span><span class="nx">escape</span><span class="p">,</span><span class="w"> </span><span class="nx">escapeInd</span><span class="p">];</span> +<span class="p">}</span> + +<span class="kd">function</span><span class="w"> </span><span class="nx">nBodyStep</span><span class="p">(</span><span class="nx">coords</span><span class="p">,</span><span class="w"> </span><span class="nx">masses</span><span class="p">,</span><span class="w"> </span><span class="nx">deltaT</span><span class="p">,</span><span class="w"> </span><span class="nx">maxSep</span><span class="p">,</span><span class="w"> </span><span class="nx">nBodies</span><span class="p">,</span><span class="w"> </span><span class="nx">G</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">6.67408313131313e-11</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// Similar to our step function before, but keeping track of collisions</span> +<span class="w"> </span><span class="nx">coords</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">step</span><span class="p">(</span><span class="nx">coords</span><span class="p">,</span><span class="w"> </span><span class="nx">masses</span><span class="p">,</span><span class="w"> </span><span class="nx">deltaT</span><span class="p">,</span><span class="w"> </span><span class="nx">nBodies</span><span class="p">,</span><span class="w"> </span><span class="nx">G</span><span class="p">);</span><span class="w"> </span><span class="c1">// Update the positions as we did before</span> +<span class="w"> </span><span class="c1">//console.log(detectCollisionsEscape(coords, deltaT, maxSep));</span> +<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="p">[</span><span class="nx">collision</span><span class="p">,</span><span class="w"> </span><span class="nx">collisionInds</span><span class="p">,</span><span class="w"> </span><span class="nx">escape</span><span class="p">,</span><span class="w"> </span><span class="nx">escapeInd</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">detectCollisionsEscape</span><span class="p">(</span><span class="nx">coords</span><span class="p">,</span><span class="w"> </span><span class="nx">deltaT</span><span class="p">,</span><span class="w"> </span><span class="nx">maxSep</span><span class="p">);</span><span class="w"> </span><span class="c1">// Detect collisions/escapes</span> + + +<span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">collision</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// Do inelastic collision and delete extra body (2 -> 1)</span> +<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="p">[</span><span class="nx">i1</span><span class="p">,</span><span class="w"> </span><span class="nx">i2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">collisionInds</span><span class="p">;</span> +<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="p">[</span><span class="nx">x1</span><span class="p">,</span><span class="w"> </span><span class="nx">x2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="nx">coords</span><span class="p">[</span><span class="mf">0</span><span class="p">][</span><span class="nx">i1</span><span class="p">],</span><span class="w"> </span><span class="nx">coords</span><span class="p">[</span><span class="mf">0</span><span class="p">][</span><span class="nx">i2</span><span class="p">]];</span> +<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="p">[</span><span class="nx">y1</span><span class="p">,</span><span class="w"> </span><span class="nx">y2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="nx">coords</span><span class="p">[</span><span class="mf">1</span><span class="p">][</span><span class="nx">i1</span><span class="p">],</span><span class="w"> </span><span class="nx">coords</span><span class="p">[</span><span class="mf">1</span><span class="p">][</span><span class="nx">i2</span><span class="p">]];</span> +<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="p">[</span><span class="nx">vx1</span><span class="p">,</span><span class="w"> </span><span class="nx">vx2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="nx">coords</span><span class="p">[</span><span class="mf">2</span><span class="p">][</span><span class="nx">i1</span><span class="p">],</span><span class="w"> </span><span class="nx">coords</span><span class="p">[</span><span class="mf">2</span><span class="p">][</span><span class="nx">i2</span><span class="p">]];</span> +<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="p">[</span><span class="nx">vy1</span><span class="p">,</span><span class="w"> </span><span class="nx">vy2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="nx">coords</span><span class="p">[</span><span class="mf">3</span><span class="p">][</span><span class="nx">i1</span><span class="p">],</span><span class="w"> </span><span class="nx">coords</span><span class="p">[</span><span class="mf">3</span><span class="p">][</span><span class="nx">i2</span><span class="p">]];</span> +<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="p">[</span><span class="nx">px1</span><span class="p">,</span><span class="w"> </span><span class="nx">px2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="nx">masses</span><span class="p">[</span><span class="nx">i1</span><span class="p">]</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">vx1</span><span class="p">,</span><span class="w"> </span><span class="nx">masses</span><span class="p">[</span><span class="nx">i2</span><span class="p">]</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">vx2</span><span class="p">];</span> +<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="p">[</span><span class="nx">py1</span><span class="p">,</span><span class="w"> </span><span class="nx">py2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="nx">masses</span><span class="p">[</span><span class="nx">i1</span><span class="p">]</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">vy1</span><span class="p">,</span><span class="w"> </span><span class="nx">masses</span><span class="p">[</span><span class="nx">i2</span><span class="p">]</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">vy2</span><span class="p">];</span> +<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">px</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">px1</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">px2</span><span class="p">;</span> +<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">py</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">py1</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">py2</span><span class="p">;</span> +<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">newM</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">masses</span><span class="p">[</span><span class="nx">i1</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">masses</span><span class="p">[</span><span class="nx">i2</span><span class="p">];</span> +<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">vfx</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">px</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="nx">newM</span><span class="p">;</span> +<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">vfy</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">py</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="nx">newM</span><span class="p">;</span> +<span class="w"> </span><span class="nx">coords</span><span class="p">[</span><span class="mf">0</span><span class="p">][</span><span class="nx">i1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="nx">x1</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">masses</span><span class="p">[</span><span class="nx">i1</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">x2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">masses</span><span class="p">[</span><span class="nx">i2</span><span class="p">])</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="p">(</span><span class="nx">masses</span><span class="p">[</span><span class="nx">i1</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">masses</span><span class="p">[</span><span class="nx">i2</span><span class="p">]);</span><span class="w"> </span><span class="c1">// Center of mass</span> +<span class="w"> </span><span class="nx">coords</span><span class="p">[</span><span class="mf">1</span><span class="p">][</span><span class="nx">i1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="nx">y1</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">masses</span><span class="p">[</span><span class="nx">i1</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">y2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">masses</span><span class="p">[</span><span class="nx">i2</span><span class="p">])</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="p">(</span><span class="nx">masses</span><span class="p">[</span><span class="nx">i1</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">masses</span><span class="p">[</span><span class="nx">i2</span><span class="p">]);</span> +<span class="w"> </span><span class="nx">coords</span><span class="p">[</span><span class="mf">2</span><span class="p">][</span><span class="nx">i1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">vfx</span><span class="p">;</span> +<span class="w"> </span><span class="nx">coords</span><span class="p">[</span><span class="mf">3</span><span class="p">][</span><span class="nx">i1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">vfy</span><span class="p">;</span> +<span class="w"> </span><span class="nx">coords</span><span class="p">[</span><span class="mf">0</span><span class="p">].</span><span class="nx">splice</span><span class="p">(</span><span class="nx">i2</span><span class="p">,</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span> +<span class="w"> </span><span class="nx">coords</span><span class="p">[</span><span class="mf">1</span><span class="p">].</span><span class="nx">splice</span><span class="p">(</span><span class="nx">i2</span><span class="p">,</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span> +<span class="w"> </span><span class="nx">coords</span><span class="p">[</span><span class="mf">2</span><span class="p">].</span><span class="nx">splice</span><span class="p">(</span><span class="nx">i2</span><span class="p">,</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span> +<span class="w"> </span><span class="nx">coords</span><span class="p">[</span><span class="mf">3</span><span class="p">].</span><span class="nx">splice</span><span class="p">(</span><span class="nx">i2</span><span class="p">,</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span> +<span class="w"> </span><span class="nx">masses</span><span class="p">[</span><span class="nx">i1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">newM</span><span class="p">;</span> +<span class="w"> </span><span class="nx">masses</span><span class="p">.</span><span class="nx">splice</span><span class="p">(</span><span class="nx">i2</span><span class="p">,</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span> +<span class="w"> </span><span class="nx">nBodies</span><span class="o">--</span><span class="p">;</span> +<span class="w"> </span><span class="p">}</span> +<span class="w"> </span><span class="c1">// Could also implement condition for escape where we stop calculating forces but I'm too lazy for now</span> +<span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="p">[</span><span class="nx">coords</span><span class="p">,</span><span class="w"> </span><span class="nx">masses</span><span class="p">,</span><span class="w"> </span><span class="nx">nBodies</span><span class="p">,</span><span class="w"> </span><span class="nx">collision</span><span class="p">,</span><span class="w"> </span><span class="nx">collisionInds</span><span class="p">,</span><span class="w"> </span><span class="nx">escape</span><span class="p">,</span><span class="w"> </span><span class="nx">escapeInd</span><span class="p">];</span> +<span class="p">}</span> + +<span class="kd">function</span><span class="w"> </span><span class="nx">uniform</span><span class="p">(</span><span class="nx">min</span><span class="p">,</span><span class="w"> </span><span class="nx">max</span><span class="p">)</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">random</span><span class="p">()</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="nx">max</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">min</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">min</span><span class="p">;</span> +<span class="p">}</span> + +<span class="kd">function</span><span class="w"> </span><span class="nx">deepCopyCoordsArray</span><span class="p">(</span><span class="nx">arr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">arr</span><span class="p">.</span><span class="nx">map</span><span class="p">(</span><span class="nx">innerArr</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="nx">innerArr</span><span class="p">.</span><span class="nx">slice</span><span class="p">());</span> +<span class="p">}</span> + +<span class="kd">function</span><span class="w"> </span><span class="nx">genNBodyResults</span><span class="p">(</span><span class="nx">nBodies</span><span class="p">,</span><span class="w"> </span><span class="nx">tStop</span><span class="p">,</span><span class="w"> </span><span class="nx">nTPts</span><span class="p">,</span><span class="w"> </span><span class="nx">nBodiesStop</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">10</span><span class="p">,</span><span class="w"> </span><span class="nx">G</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">6.67408313131313e-11</span><span class="p">)</span><span class="w"> </span><span class="p">{</span> + +<span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nx">btn</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">document</span><span class="p">.</span><span class="nx">getElementById</span><span class="p">(</span><span class="s2">"startSim3"</span><span class="p">);</span> +<span class="w"> </span><span class="c1">// Set button text to Solving</span> +<span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nx">prevText</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">btn</span><span class="p">.</span><span class="nx">innerHTML</span><span class="p">;</span> +<span class="w"> </span><span class="nx">btn</span><span class="p">.</span><span class="nx">innerHTML</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s2">"Solving..."</span><span class="p">;</span> + +<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">coords</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="nb">Array</span><span class="p">(</span><span class="nx">nBodies</span><span class="p">).</span><span class="nx">fill</span><span class="p">(</span><span class="mf">0</span><span class="p">),</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">nBodies</span><span class="p">).</span><span class="nx">fill</span><span class="p">(</span><span class="mf">0</span><span class="p">),</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">nBodies</span><span class="p">).</span><span class="nx">fill</span><span class="p">(</span><span class="mf">0</span><span class="p">),</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">nBodies</span><span class="p">).</span><span class="nx">fill</span><span class="p">(</span><span class="mf">0</span><span class="p">)];</span> +<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">Mstar</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">2e30</span><span class="p">;</span> +<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">Mp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">Mstar</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">1e4</span><span class="p">;</span> + +<span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">nBodies</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// Initialize coordinates on ~Keplerian orbits</span> +<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">accept</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">false</span><span class="p">;</span> +<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span> +<span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="nx">accept</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// Prevent a particle from spawning within 0.2 AU too close to "star"</span> +<span class="w"> </span><span class="nx">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">random</span><span class="p">()</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mf">1.5e11</span><span class="p">;</span><span class="w"> </span><span class="c1">// Say radius of 2 AU</span> +<span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">r</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">1.5e11</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="mf">0.2</span><span class="p">)</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="nx">accept</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">true</span><span class="p">;</span> +<span class="w"> </span><span class="p">}</span> +<span class="w"> </span><span class="p">}</span> +<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">theta</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">uniform</span><span class="p">(</span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">PI</span><span class="p">);</span> +<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">x</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">r</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">cos</span><span class="p">(</span><span class="nx">theta</span><span class="p">);</span> +<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">y</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">r</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">sin</span><span class="p">(</span><span class="nx">theta</span><span class="p">);</span> +<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">v</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">sqrt</span><span class="p">(</span><span class="nx">G</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">Mstar</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="nx">r</span><span class="p">);</span> +<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">perturbedV</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">v</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">v</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">1000</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">uniform</span><span class="p">(</span><span class="o">-</span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span><span class="w"> </span><span class="c1">// Perturb the velocities ever so slightly</span> +<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">vTheta</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">atan2</span><span class="p">(</span><span class="nx">y</span><span class="p">,</span><span class="w"> </span><span class="nx">x</span><span class="p">);</span> +<span class="w"> </span><span class="nx">coords</span><span class="p">[</span><span class="mf">0</span><span class="p">][</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">x</span><span class="p">;</span> +<span class="w"> </span><span class="nx">coords</span><span class="p">[</span><span class="mf">1</span><span class="p">][</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">y</span><span class="p">;</span> +<span class="w"> </span><span class="nx">coords</span><span class="p">[</span><span class="mf">2</span><span class="p">][</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">-</span><span class="nx">perturbedV</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">sin</span><span class="p">(</span><span class="nx">vTheta</span><span class="p">);</span> +<span class="w"> </span><span class="nx">coords</span><span class="p">[</span><span class="mf">3</span><span class="p">][</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">perturbedV</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">cos</span><span class="p">(</span><span class="nx">vTheta</span><span class="p">);</span> +<span class="w"> </span><span class="p">}</span> + +<span class="w"> </span><span class="c1">//console.log('Initial coords:', coords);</span> + + +<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">masses</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">nBodies</span><span class="p">).</span><span class="nx">fill</span><span class="p">(</span><span class="nx">Mp</span><span class="p">);</span><span class="w"> </span><span class="c1">// Initialize masses</span> +<span class="w"> </span><span class="nx">masses</span><span class="p">[</span><span class="mf">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">Mstar</span><span class="p">;</span><span class="w"> </span><span class="c1">// Make index one special as the central star</span> +<span class="w"> </span><span class="nx">coords</span><span class="p">[</span><span class="mf">0</span><span class="p">][</span><span class="mf">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span> +<span class="w"> </span><span class="nx">coords</span><span class="p">[</span><span class="mf">1</span><span class="p">][</span><span class="mf">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span> +<span class="w"> </span><span class="nx">coords</span><span class="p">[</span><span class="mf">2</span><span class="p">][</span><span class="mf">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span> +<span class="w"> </span><span class="nx">coords</span><span class="p">[</span><span class="mf">3</span><span class="p">][</span><span class="mf">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// Initialize central star at origin with no velocity</span> +<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">yearSec</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">365</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mf">24</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mf">3600</span><span class="p">;</span> +<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">time</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">.</span><span class="kr">from</span><span class="p">({</span><span class="w"> </span><span class="nx">length</span><span class="o">:</span><span class="w"> </span><span class="nx">nTPts</span><span class="w"> </span><span class="p">},</span><span class="w"> </span><span class="p">(</span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">tStop</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="p">(</span><span class="nx">nTPts</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">yearSec</span><span class="p">);</span><span class="w"> </span><span class="c1">// Years -> s</span> +<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">t</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">time</span><span class="p">[</span><span class="mf">0</span><span class="p">];</span> +<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">deltaT</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">time</span><span class="p">[</span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">time</span><span class="p">[</span><span class="mf">0</span><span class="p">];</span> +<span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">tInd</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span> +<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">coordsRecord</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="nx">deepCopyCoordsArray</span><span class="p">(</span><span class="nx">coords</span><span class="p">)];</span> +<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">massRecord</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="nx">masses</span><span class="p">.</span><span class="nx">slice</span><span class="p">()];</span><span class="w"> </span><span class="c1">// Initialize records with initial conditions</span> + + +<span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">tInd</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">nTPts</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="nx">nBodies</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="nx">nBodiesStop</span><span class="p">)</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="c1">//console.log('Initial coords:', coords);</span> +<span class="w"> </span><span class="p">[</span><span class="nx">coords</span><span class="p">,</span><span class="w"> </span><span class="nx">masses</span><span class="p">,</span><span class="w"> </span><span class="nx">nBodies</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nBodyStep</span><span class="p">(</span><span class="nx">coords</span><span class="p">,</span><span class="w"> </span><span class="nx">masses</span><span class="p">,</span><span class="w"> </span><span class="nx">deltaT</span><span class="p">,</span><span class="w"> </span><span class="mf">10</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mf">1.5e11</span><span class="p">,</span><span class="w"> </span><span class="nx">nBodies</span><span class="p">,</span><span class="w"> </span><span class="nx">G</span><span class="p">);</span><span class="w"> </span><span class="c1">// Update</span> +<span class="w"> </span><span class="nx">coordsRecord</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">deepCopyCoordsArray</span><span class="p">(</span><span class="nx">coords</span><span class="p">));</span> +<span class="w"> </span><span class="nx">massRecord</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">masses</span><span class="p">.</span><span class="nx">slice</span><span class="p">());</span><span class="w"> </span><span class="c1">// Add to records</span> +<span class="w"> </span><span class="nx">tInd</span><span class="o">++</span><span class="p">;</span> +<span class="w"> </span><span class="nx">t</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">time</span><span class="p">[</span><span class="nx">tInd</span><span class="p">];</span> +<span class="w"> </span><span class="c1">//console.log(`currently at t = ${(t / yearSec).toFixed(2)} years\r`);</span> +<span class="w"> </span><span class="p">}</span> +<span class="w"> </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="sb">`final time = </span><span class="si">${</span><span class="nx">time</span><span class="p">[</span><span class="nx">tInd</span><span class="p">]</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="nx">yearSec</span><span class="si">}</span><span class="sb"> years with </span><span class="si">${</span><span class="nx">nBodies</span><span class="si">}</span><span class="sb"> bodies remaining`</span><span class="p">);</span> + +<span class="w"> </span><span class="c1">// Set button text to Start Simulation</span> +<span class="w"> </span><span class="nx">btn</span><span class="p">.</span><span class="nx">innerHTML</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">prevText</span><span class="p">;</span> + +<span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="p">[</span><span class="nx">coordsRecord</span><span class="p">,</span><span class="w"> </span><span class="nx">massRecord</span><span class="p">,</span><span class="w"> </span><span class="nx">time</span><span class="p">.</span><span class="nx">slice</span><span class="p">(</span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="nx">tInd</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">)];</span> +<span class="p">}</span> + + +<span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="p">[</span><span class="nx">coordsRecordR</span><span class="p">,</span><span class="w"> </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">tR</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">genNBodyResults</span><span class="p">(</span><span class="mf">256</span><span class="p">,</span><span class="mf">1</span><span class="p">,</span><span class="mf">1001</span><span class="p">);</span> +<span class="w"> </span><span class="c1">//console.log(coordsRecordR);</span> +<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">yearSec</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">365</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mf">24</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mf">3600</span><span class="p">;</span> + +<span class="w"> </span><span class="kd">function</span><span class="w"> </span><span class="nx">createFrame</span><span class="p">(</span><span class="nx">coordsR</span><span class="p">)</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="nx">coordsR</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="o">!</span><span class="nx">coordsR</span><span class="p">[</span><span class="mf">0</span><span class="p">]</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="o">!</span><span class="nx">coordsR</span><span class="p">[</span><span class="mf">1</span><span class="p">])</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="p">[];</span> +<span class="w"> </span><span class="p">}</span> + +<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">traceCentralStar</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="nx">x</span><span class="o">:</span><span class="w"> </span><span class="p">[</span><span class="nx">coordsR</span><span class="p">[</span><span class="mf">0</span><span class="p">][</span><span class="mf">0</span><span class="p">]</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">1.5e11</span><span class="p">],</span> +<span class="w"> </span><span class="nx">y</span><span class="o">:</span><span class="w"> </span><span class="p">[</span><span class="nx">coordsR</span><span class="p">[</span><span class="mf">1</span><span class="p">][</span><span class="mf">0</span><span class="p">]</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">1.5e11</span><span class="p">],</span> +<span class="w"> </span><span class="nx">mode</span><span class="o">:</span><span class="w"> </span><span class="s1">'markers'</span><span class="p">,</span> +<span class="w"> </span><span class="nx">type</span><span class="o">:</span><span class="w"> </span><span class="s1">'scatter'</span><span class="p">,</span> +<span class="w"> </span><span class="nx">name</span><span class="o">:</span><span class="w"> </span><span class="s1">'Central star'</span><span class="p">,</span> +<span class="w"> </span><span class="nx">marker</span><span class="o">:</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nx">color</span><span class="o">:</span><span class="w"> </span><span class="s1">'gold'</span><span class="p">,</span><span class="w"> </span><span class="nx">symbol</span><span class="o">:</span><span class="w"> </span><span class="s1">'star'</span><span class="p">,</span><span class="w"> </span><span class="nx">size</span><span class="o">:</span><span class="w"> </span><span class="mf">10</span><span class="w"> </span><span class="p">},</span> +<span class="w"> </span><span class="p">};</span> + +<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">xCoords</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">coordsR</span><span class="p">[</span><span class="mf">0</span><span class="p">].</span><span class="nx">slice</span><span class="p">(</span><span class="mf">1</span><span class="p">).</span><span class="nx">map</span><span class="p">(</span><span class="nx">x</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="nx">x</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">1.5e11</span><span class="p">);</span> +<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">yCoords</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">coordsR</span><span class="p">[</span><span class="mf">1</span><span class="p">].</span><span class="nx">slice</span><span class="p">(</span><span class="mf">1</span><span class="p">).</span><span class="nx">map</span><span class="p">(</span><span class="nx">y</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="nx">y</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">1.5e11</span><span class="p">);</span> + +<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">traceOtherBodies</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="nx">x</span><span class="o">:</span><span class="w"> </span><span class="nx">xCoords</span><span class="p">,</span> +<span class="w"> </span><span class="nx">y</span><span class="o">:</span><span class="w"> </span><span class="nx">yCoords</span><span class="p">,</span> +<span class="w"> </span><span class="nx">mode</span><span class="o">:</span><span class="w"> </span><span class="s1">'markers'</span><span class="p">,</span> +<span class="w"> </span><span class="nx">type</span><span class="o">:</span><span class="w"> </span><span class="s1">'scatter'</span><span class="p">,</span> +<span class="w"> </span><span class="nx">name</span><span class="o">:</span><span class="w"> </span><span class="s1">''</span><span class="p">,</span> +<span class="w"> </span><span class="nx">marker</span><span class="o">:</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nx">color</span><span class="o">:</span><span class="w"> </span><span class="s1">'dodgerblue'</span><span class="p">,</span><span class="w"> </span><span class="nx">symbol</span><span class="o">:</span><span class="w"> </span><span class="s1">'circle'</span><span class="p">,</span><span class="w"> </span><span class="nx">size</span><span class="o">:</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="p">},</span> +<span class="w"> </span><span class="p">};</span> + +<span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="p">[</span><span class="nx">traceCentralStar</span><span class="p">,</span><span class="w"> </span><span class="nx">traceOtherBodies</span><span class="p">];</span> +<span class="w"> </span><span class="p">}</span> + + +<span class="w"> </span><span class="kd">function</span><span class="w"> </span><span class="nx">createLayout</span><span class="p">(</span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="nx">title</span><span class="o">:</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="nx">text</span><span class="o">:</span><span class="w"> </span><span class="sb">`N-Body Problem: t = </span><span class="si">${</span><span class="nb">Number</span><span class="p">(</span><span class="nx">t</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="nx">yearSec</span><span class="p">).</span><span class="nx">toFixed</span><span class="p">(</span><span class="mf">3</span><span class="p">)</span><span class="si">}</span><span class="sb"> years`</span><span class="p">,</span> +<span class="w"> </span><span class="nx">x</span><span class="o">:</span><span class="w"> </span><span class="mf">0.03</span><span class="p">,</span> +<span class="w"> </span><span class="nx">y</span><span class="o">:</span><span class="w"> </span><span class="mf">0.97</span><span class="p">,</span> +<span class="w"> </span><span class="nx">xanchor</span><span class="o">:</span><span class="w"> </span><span class="s1">'left'</span><span class="p">,</span> +<span class="w"> </span><span class="nx">yanchor</span><span class="o">:</span><span class="w"> </span><span class="s1">'top'</span><span class="p">,</span> +<span class="w"> </span><span class="nx">font</span><span class="o">:</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nx">size</span><span class="o">:</span><span class="w"> </span><span class="mf">14</span><span class="w"> </span><span class="p">},</span> +<span class="w"> </span><span class="p">},</span> +<span class="w"> </span><span class="nx">xaxis</span><span class="o">:</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nx">title</span><span class="o">:</span><span class="w"> </span><span class="s1">'x [AU]'</span><span class="p">,</span><span class="w"> </span><span class="nx">range</span><span class="o">:</span><span class="w"> </span><span class="p">[</span><span class="o">-</span><span class="mf">2.1</span><span class="p">,</span><span class="w"> </span><span class="mf">2.1</span><span class="p">]</span><span class="w"> </span><span class="p">},</span> +<span class="w"> </span><span class="nx">yaxis</span><span class="o">:</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nx">title</span><span class="o">:</span><span class="w"> </span><span class="s1">'y [AU]'</span><span class="p">,</span><span class="w"> </span><span class="nx">range</span><span class="o">:</span><span class="w"> </span><span class="p">[</span><span class="o">-</span><span class="mf">2.1</span><span class="p">,</span><span class="w"> </span><span class="mf">2.1</span><span class="p">],</span><span class="w"> </span><span class="nx">scaleanchor</span><span class="o">:</span><span class="w"> </span><span class="s1">'x'</span><span class="p">,</span><span class="w"> </span><span class="nx">scaleratio</span><span class="o">:</span><span class="w"> </span><span class="mf">1</span><span class="w"> </span><span class="p">},</span> +<span class="w"> </span><span class="nx">showlegend</span><span class="o">:</span><span class="w"> </span><span class="kc">false</span><span class="p">,</span> +<span class="w"> </span><span class="nx">margin</span><span class="o">:</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="nx">l</span><span class="o">:</span><span class="w"> </span><span class="mf">60</span><span class="p">,</span><span class="w"> </span><span class="nx">r</span><span class="o">:</span><span class="w"> </span><span class="mf">40</span><span class="p">,</span><span class="w"> </span><span class="nx">t</span><span class="o">:</span><span class="w"> </span><span class="mf">40</span><span class="p">,</span><span class="w"> </span><span class="nx">b</span><span class="o">:</span><span class="w"> </span><span class="mf">40</span><span class="w"> </span><span class="p">},</span> +<span class="w"> </span><span class="nx">width</span><span class="o">:</span><span class="w"> </span><span class="mf">800</span><span class="p">,</span> +<span class="w"> </span><span class="nx">height</span><span class="o">:</span><span class="w"> </span><span class="mf">800</span><span class="p">,</span> +<span class="w"> </span><span class="nx">plot_bgcolor</span><span class="o">:</span><span class="w"> </span><span class="s1">'black'</span><span class="p">,</span> +<span class="w"> </span><span class="p">};</span> +<span class="p">}</span> + +<span class="w"> </span><span class="kd">function</span><span class="w"> </span><span class="nx">animateNBodyProblem</span><span class="p">()</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">nFrames</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">tR</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span> + +<span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">nFrames</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">frameData</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">createFrame</span><span class="p">(</span><span class="nx">coordsRecordR</span><span class="p">[</span><span class="nx">i</span><span class="p">]);</span> +<span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">layout</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">createLayout</span><span class="p">(</span><span class="nx">i</span><span class="p">);</span> +<span class="w"> </span><span class="c1">//Plotly.newPlot(plotDiv, frameData, layout);</span> +<span class="w"> </span><span class="k">try</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="nx">Plotly</span><span class="p">.</span><span class="nx">animate</span><span class="p">(</span><span class="s2">"plot"</span><span class="p">,</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="nx">data</span><span class="o">:</span><span class="w"> </span><span class="nx">frameData</span><span class="p">,</span><span class="w"> </span><span class="nx">layout</span><span class="o">:</span><span class="w"> </span><span class="nx">layout</span> +<span class="w"> </span><span class="p">},</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="nx">staticPlot</span><span class="o">:</span><span class="w"> </span><span class="kc">true</span><span class="p">,</span> +<span class="w"> </span><span class="nx">transition</span><span class="o">:</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="nx">duration</span><span class="o">:</span><span class="w"> </span><span class="mf">0</span><span class="p">,</span> +<span class="w"> </span><span class="p">},</span> +<span class="w"> </span><span class="nx">frame</span><span class="o">:</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="nx">duration</span><span class="o">:</span><span class="w"> </span><span class="mf">0</span><span class="p">,</span> +<span class="w"> </span><span class="nx">redraw</span><span class="o">:</span><span class="w"> </span><span class="kc">false</span><span class="p">,</span> +<span class="w"> </span><span class="p">}</span> +<span class="w"> </span><span class="p">});</span> +<span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">catch</span><span class="w"> </span><span class="p">(</span><span class="nx">err</span><span class="p">)</span><span class="w"> </span><span class="p">{</span> +<span class="w"> </span><span class="nx">Plotly</span><span class="p">.</span><span class="nx">newPlot</span><span class="p">(</span><span class="s1">'plot'</span><span class="p">,</span><span class="w"> </span><span class="nx">frameData</span><span class="p">,</span><span class="w"> </span><span class="nx">layout</span><span class="p">);</span> +<span class="w"> </span><span class="p">}</span> +<span class="w"> </span><span class="p">}</span> +<span class="p">}</span> + +<span class="nx">animateNBodyProblem</span><span class="p">();</span> </code></pre> </div> <h2>Playground</h2> <script src="https://cdn.plot.ly/plotly-latest.min.js"></script> + <script src="https://cdnjs.cloudflare.com/ajax/libs/mathjs/11.8.0/math.js"></script> + <script src="/assets/n-body/script.js"></script> + <div id="main-plot-div"> <noscript> The simulations require JavaScript to be viewed properly :( @@ -705,10 +710,12 @@ The simulations require JavaScript to be viewed properly :( <input type="number" min="1" max="10000" value="7e3" id="vRange"> </div> -<button type="button" id="startSim1" onclick="plotEarthSun()">Sun-Earth Orbit</button> + +<p><button type="button" id="startSim1" onclick="plotEarthSun()">Sun-Earth Orbit</button> <button type="button" id="startSim2" onclick="plotClassic3BodyProblem()">Classic 3-Body Problem</button> <button type="button" id="startSim3" onclick="plotRandomNBodySimulation()">Random n-Body Simulation</button> -<button type="button" id="startSim4" onclick="plotRandom3BodySimulation()">Random 3-Body Simulation</button> +<button type="button" id="startSim4" onclick="plotRandom3BodySimulation()">Random 3-Body Simulation</button></p> + <script> function clearAl() { plotOrbit = false; |