diff options
Diffstat (limited to 'docs')
| -rw-r--r-- | docs/assets/n-body/script.js | 112 | ||||
| -rw-r--r-- | docs/feed.rss | 42 | ||||
| -rw-r--r-- | docs/posts/2023-04-30-n-body-simulation.html | 38 |
3 files changed, 165 insertions, 27 deletions
diff --git a/docs/assets/n-body/script.js b/docs/assets/n-body/script.js index e87d92c..6042e27 100644 --- a/docs/assets/n-body/script.js +++ b/docs/assets/n-body/script.js @@ -2,6 +2,7 @@ var plotOrbit = true var plotClassic = false var plotRandom = false +var plotRandom3Body = false var plotIndex = 0 var delay = 10 var tailLength = 1; @@ -288,6 +289,36 @@ function initCondGen(nBodies, vRange = [-7e3, 7e3], posRange = [-35, 35]) { return {m: m.map(x => x * 2e30), rad: rad.map(x => x * 7e8), coords: coords}; } +function random3BodySimSolver(tStop, nTPts, nBodiesStop=2, G=6.674e-11) { + let initConditions = initCondGen(3,[-7e3, 7e3],[-5, 5]); + let myMasses = initConditions.m; + let myCoords = initConditions.coords; + + let nBodies3B = 3; + + const yearSec = 365 * 24 * 3600; + + const time = Array.from({ length: nTPts }, (_, i) => i * tStop / (nTPts - 1) * yearSec); // Years -> s + let t = time[0]; + const deltaT = time[1] - time[0]; + let tInd = 0; + const coordsRecord = [deepCopyCoordsArray(myCoords)]; + const massRecord = [myMasses.slice()]; // Initialize records with initial conditions + + while (tInd < nTPts && nBodies3B > nBodiesStop) { + [myCoords, myMasses, nBodies3B] = nBodyStep(myCoords, myMasses, deltaT, 10 * 1.5e11, nBodies3B, G); // Update + coordsRecord.push(deepCopyCoordsArray(myCoords)); + massRecord.push(myMasses.slice()); // Add to records + tInd++; + t = time[tInd]; + } + + console.log(nBodies3B) + + return [coordsRecord, massRecord, time.slice(0, tInd + 1)]; + +} + function calculateAndPlot() { try { @@ -413,8 +444,8 @@ function calculateAndPlot() { yaxis: { title: 'y [AU]', range: [-2.1, 2.1], scaleanchor: 'x', scaleratio: 1 }, showlegend: false, margin: { l: 60, r: 40, t: 40, b: 40 }, - width: 800, - height: 800, + //width: 800, + //height: 800, plot_bgcolor: 'black', }; } @@ -448,6 +479,79 @@ function calculateAndPlot() { animateNBodyProblem(); + } else if (plotRandom3Body==true) { + let [coordsRecord3, _, t3] = random3BodySimSolver(1,1000); + + const yearSec = 365 * 24 * 3600; + + function createFrame(coords3) { + if (!coords3 || !coords3[0] || !coords3[1]) { + return []; + } + + const xCoords = coords3[0].slice(0).map(x => x / 1.5e11); + const yCoords = coords3[1].slice(0).map(y => y / 1.5e11); + + const traceOtherBodies = { + x: xCoords, + y: yCoords, + mode: 'markers', + type: 'scatter', + name: '', + marker: { color: 'dodgerblue', symbol: 'circle', size: 5 }, + }; + + return [traceOtherBodies]; + } + + function createLayout(i) { + return { + title: { + text: `3-Body Problem`,//= ${Number(t[i] / yearSec).toFixed(3)} years`, + x: 0.03, + y: 0.97, + xanchor: 'left', + yanchor: 'top', + font: { size: 14 }, + }, + xaxis: { title: 'x [AU]' }, + yaxis: { title: 'y [AU]', scaleanchor: 'x', scaleratio: 1 }, + showlegend: false, + margin: { l: 60, r: 40, t: 40, b: 40 }, + //width: 800, + //height: 800, + plot_bgcolor: 'black', + }; + } + + function animate3BodyProblem() { + const nFrames = t3.length; + + for (let i = 0; i < nFrames; i++) { + const frameData = createFrame(coordsRecord3[i]); + const layout = createLayout(i); + //Plotly.newPlot(plotDiv, frameData, layout); + try { + Plotly.animate("plot", { + data: frameData, layout: layout + }, { + staticPlot: true, + transition: { + duration: 0, + }, + frame: { + duration: 0, + redraw: false, + } + }); + } catch (err) { + Plotly.newPlot('plot', frameData, layout); + } + } + } + + animate3BodyProblem(); + } else if (plotClassic==true) { // Initial conditions setup let M = [1, 1, 1]; @@ -478,11 +582,12 @@ animateNBodyProblem(); VX.forEach((_, idx) => VX[idx][i] = coords[2][idx]); VY.forEach((_, idx) => VY[idx][i] = coords[3][idx]); } + function plotClassicFunc() { var tailLength = 1; if (plotIndex < tailLength) { tailLength = 0; - } else if (plotIndex > time.length) { + } if (plotIndex > time.length) { plotIndex = 0; } else { tailLength = plotIndex - tailLength; @@ -493,6 +598,7 @@ animateNBodyProblem(); try { time[currentIndex].toFixed(3); } catch (e) { + console.log(e) currentIndex = 0; } diff --git a/docs/feed.rss b/docs/feed.rss index 760ae20..23f6a2f 100644 --- a/docs/feed.rss +++ b/docs/feed.rss @@ -4,8 +4,8 @@ <title>Navan's Archive</title> <description>Rare Tips, Tricks and Posts</description> <link>https://web.navan.dev/</link><language>en</language> - <lastBuildDate>Mon, 01 May 2023 00:26:41 -0000</lastBuildDate> - <pubDate>Mon, 01 May 2023 00:26:41 -0000</pubDate> + <lastBuildDate>Mon, 01 May 2023 12:58:21 -0000</lastBuildDate> + <pubDate>Mon, 01 May 2023 12:58:21 -0000</pubDate> <ttl>250</ttl> <atom:link href="https://web.navan.dev/feed.rss" rel="self" type="application/rss+xml"/> @@ -4147,10 +4147,10 @@ Seeing that you are reading this on Mastodon, and that I have updated this secti <p>Workflow:</p> <ul> -<li><p>Understand the problem</p></li> -<li><p>Visualise a basic orbit</p></li> -<li><p>Solve and plot the classic figure-8 orbit</p></li> -<li><p>random n-body solution generator</p></li> +<li>Understand the problem</li> +<li>Visualise a basic orbit</li> +<li>Solve and plot the classic figure-8 orbit</li> +<li>Random n-body solution generator</li> </ul> <p><strong>To workaround memory issues, the simulations are only run on-demand when the user clicks the respective button. Scroll down to the bottom of the page to see the results.</strong></p> @@ -4161,7 +4161,7 @@ Seeing that you are reading this on Mastodon, and that I have updated this secti <p>Imagine you are observing a <em>cosmic dance</em> between multiple celestial bodies, all tugging on one another as they move through space. The n-body problem aims to undersand and predict the paths of these objects as they move through space.</p> -<p>When <code>n=2</code>, i.e we have only two objects, say the Earth and the Moon, we can easily apply Newtonian physics to predict their motion. However, when <code>n>2</code>, the problem becomes much more difficult to solve analytically. This is because each object feels the gravitational pull from all other objects, and thus the equations of motion become coupled and non-linear. </p> +<p>When <code>n=2</code>, i.e we have only two objects, say the Earth and the Moon, we can easily apply Newtonian physics to predict their motion. However, when <code>n>2</code>, the problem becomes much more difficult to solve analytically.[1] This is because each object feels the gravitational pull from all other objects, and thus the equations of motion become coupled and non-linear. </p> <p>As the number of objects increases, finding an exact solution becomes impossible, and we rely on analyticals approximations.</p> @@ -4307,7 +4307,7 @@ Next, the function dR takes the position r and velocity v of Earth as input and <h2>Figure of 8 orbit</h2> -<p>The figure of 8 solution in the three-body problem refers to a unique and special trajectory where three celestial bodies (e.g., planets, stars) move in a figure of 8 shaped pattern around their mutual center of mass. This is special because it represents a stable and periodic solution to the three-body problem, which is known for its complexity and lack of general solutions.</p> +<p>The figure of 8 solution[2] in the three-body problem refers to a unique and special trajectory where three celestial bodies (e.g., planets, stars) move in a figure of 8 shaped pattern around their mutual center of mass. This is special because it represents a stable and periodic solution to the three-body problem, which is known for its complexity and lack of general solutions.</p> <p>In the figure of 8 solution, each of the three bodies follows the same looping path, but with a phase difference such that when one body is at one end of the loop, the other two are symmetrically positioned elsewhere along the path. The bodies maintain equal distances from each other throughout their motion, and their velocities and positions are perfectly balanced to maintain this periodic motion.</p> @@ -4773,6 +4773,10 @@ Next, the function dR takes the position r and velocity v of Earth as input and <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 :( +</noscript> + <div id="plot"></div> <label for="speedControl">Speed for 3-Body Visualisation</label> @@ -4782,12 +4786,14 @@ Next, the function dR takes the position r and velocity v of Earth as input and </div> <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="plotRandom3BodySimulation()">Random n-Body Simulation</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> <script> function clearAl() { plotOrbit = false; plotClassic = false; plotRandom = false; + plotRandom3Body = false; } function plotEarthSun() { @@ -4808,12 +4814,19 @@ function plotClassic3BodyProblem() { }, 500); } -function plotRandom3BodySimulation() { +function plotRandomNBodySimulation() { clearAl(); plotRandom = true; calculateAndPlot(); } + function plotRandom3BodySimulation() { + clearAl(); + plotRandom3Body = true; + calculateAndPlot(); + } + + </script> @@ -4828,9 +4841,12 @@ function plotRandom3BodySimulation() { </script> -<noscript> -This post requires JavaScript to be viewed properly :( -</noscript> +<h2>References</h2> + +<ol> +<li>Barrow-Green, June (2008), "The Three-Body Problem", in Gowers, Timothy; Barrow-Green, June; Leader, Imre (eds.), <em>The Princeton Companion to Mathematics</em>, Princeton University Press, pp. 726–728</li> +<li>Moore, Cristopher (1993), "Braids in classical dynamics", <em>Physical Review Letters</em>, 70 (24): 3675–3679</li> +</ol> ]]></content:encoded> </item> diff --git a/docs/posts/2023-04-30-n-body-simulation.html b/docs/posts/2023-04-30-n-body-simulation.html index 302e2e0..7d8a710 100644 --- a/docs/posts/2023-04-30-n-body-simulation.html +++ b/docs/posts/2023-04-30-n-body-simulation.html @@ -63,10 +63,10 @@ <p>Workflow:</p> <ul> -<li><p>Understand the problem</p></li> -<li><p>Visualise a basic orbit</p></li> -<li><p>Solve and plot the classic figure-8 orbit</p></li> -<li><p>random n-body solution generator</p></li> +<li>Understand the problem</li> +<li>Visualise a basic orbit</li> +<li>Solve and plot the classic figure-8 orbit</li> +<li>Random n-body solution generator</li> </ul> <p><strong>To workaround memory issues, the simulations are only run on-demand when the user clicks the respective button. Scroll down to the bottom of the page to see the results.</strong></p> @@ -77,7 +77,7 @@ <p>Imagine you are observing a <em>cosmic dance</em> between multiple celestial bodies, all tugging on one another as they move through space. The n-body problem aims to undersand and predict the paths of these objects as they move through space.</p> -<p>When <code>n=2</code>, i.e we have only two objects, say the Earth and the Moon, we can easily apply Newtonian physics to predict their motion. However, when <code>n>2</code>, the problem becomes much more difficult to solve analytically. This is because each object feels the gravitational pull from all other objects, and thus the equations of motion become coupled and non-linear. </p> +<p>When <code>n=2</code>, i.e we have only two objects, say the Earth and the Moon, we can easily apply Newtonian physics to predict their motion. However, when <code>n>2</code>, the problem becomes much more difficult to solve analytically.[1] This is because each object feels the gravitational pull from all other objects, and thus the equations of motion become coupled and non-linear. </p> <p>As the number of objects increases, finding an exact solution becomes impossible, and we rely on analyticals approximations.</p> @@ -223,7 +223,7 @@ Next, the function dR takes the position r and velocity v of Earth as input and <h2>Figure of 8 orbit</h2> -<p>The figure of 8 solution in the three-body problem refers to a unique and special trajectory where three celestial bodies (e.g., planets, stars) move in a figure of 8 shaped pattern around their mutual center of mass. This is special because it represents a stable and periodic solution to the three-body problem, which is known for its complexity and lack of general solutions.</p> +<p>The figure of 8 solution[2] in the three-body problem refers to a unique and special trajectory where three celestial bodies (e.g., planets, stars) move in a figure of 8 shaped pattern around their mutual center of mass. This is special because it represents a stable and periodic solution to the three-body problem, which is known for its complexity and lack of general solutions.</p> <p>In the figure of 8 solution, each of the three bodies follows the same looping path, but with a phase difference such that when one body is at one end of the loop, the other two are symmetrically positioned elsewhere along the path. The bodies maintain equal distances from each other throughout their motion, and their velocities and positions are perfectly balanced to maintain this periodic motion.</p> @@ -689,6 +689,10 @@ Next, the function dR takes the position r and velocity v of Earth as input and <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 :( +</noscript> + <div id="plot"></div> <label for="speedControl">Speed for 3-Body Visualisation</label> @@ -698,12 +702,14 @@ Next, the function dR takes the position r and velocity v of Earth as input and </div> <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="plotRandom3BodySimulation()">Random n-Body Simulation</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> <script> function clearAl() { plotOrbit = false; plotClassic = false; plotRandom = false; + plotRandom3Body = false; } function plotEarthSun() { @@ -724,12 +730,19 @@ function plotClassic3BodyProblem() { }, 500); } -function plotRandom3BodySimulation() { +function plotRandomNBodySimulation() { clearAl(); plotRandom = true; calculateAndPlot(); } + function plotRandom3BodySimulation() { + clearAl(); + plotRandom3Body = true; + calculateAndPlot(); + } + + </script> @@ -744,9 +757,12 @@ function plotRandom3BodySimulation() { </script> -<noscript> -This post requires JavaScript to be viewed properly :( -</noscript> +<h2>References</h2> + +<ol> +<li>Barrow-Green, June (2008), "The Three-Body Problem", in Gowers, Timothy; Barrow-Green, June; Leader, Imre (eds.), <em>The Princeton Companion to Mathematics</em>, Princeton University Press, pp. 726–728</li> +<li>Moore, Cristopher (1993), "Braids in classical dynamics", <em>Physical Review Letters</em>, 70 (24): 3675–3679</li> +</ol> <blockquote>If you have scrolled this far, consider subscribing to my mailing list <a href="https://listmonk.navan.dev/subscription/form">here.</a> You can subscribe to either a specific type of post you are interested in, or subscribe to everything with the "Everything" list.</blockquote> <script data-isso="//comments.navan.dev/" |