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06-pendulum.html
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356
06-pendulum.html
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<!--
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Copyright 2021 Matthias Müller - Ten Minute Physics
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Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:
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The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
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-->
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<!DOCTYPE html>
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<html>
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<meta name="viewport" content="width=device-width, initial-scale=1.0">
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<title>Pendulum</title>
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<style>
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body {
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font-family: verdana;
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font-size: 15px;
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}
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.button {
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background-color: #606060;
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border: none;
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color: white;
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padding: 15px 32px;
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font-size: 16px;
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margin: 4px 2px;
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cursor: pointer;
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}
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</style>
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<body>
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<button class="button" onclick="setupScene()">Restart</button>
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<button class="button" onclick="run()">Run</button>
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<button class="button" onclick="step()">Step</button>
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<p>Number of sub-steps: <input type = "range" min = "0" max = "5" value = "5" id = "stepsSlider" class = "slider"> <span id = "steps">10000</span></p>
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<canvas id = "myCanvas"></canvas>
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<script>
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var canvas = document.getElementById("myCanvas");
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var c = canvas.getContext("2d");
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canvas.width = window.innerWidth - 20;
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canvas.height = window.innerHeight - 20;
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var simMinWidth = 1.0;
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var cScale = Math.min(canvas.width, canvas.height) / simMinWidth;
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function cX(pos) { return canvas.width / 2 + pos.x * cScale; }
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function cY(pos) { return 0.4 * canvas.height - pos.y * cScale; }
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class Pendulum {
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constructor(usePBD, color, masses, lengths, angles) {
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this.usePBD = usePBD;
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this.color = color;
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this.masses = [0.0];
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this.lengths = [0.0];
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this.pos = [{x:0.0, y:0.0}];
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this.prevPos = [{x:0.0, y:0.0}];
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this.vel = [{x:0.0, y:0.0}];
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this.theta = [0.0];
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this.omega = [0.0];
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this.trail = new Int32Array(1000);
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this.trailFirst = 0;
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this.trailLast = 0;
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var x = 0.0, y = 0.0;
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for (var i = 0; i < masses.length; i++) {
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this.masses.push(masses[i]);
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this.lengths.push(lengths[i]);
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this.theta.push(angles[i]);
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this.omega.push(0.0);
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x += lengths[i] * Math.sin(angles[i]);
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y += lengths[i] * -Math.cos(angles[i]);
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this.pos.push({ x:x, y:y});
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this.prevPos.push({ x:x, y:y});
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this.vel.push({x:0, y:0});
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}
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}
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simulate(dt, gravity) {
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if (this.usePBD)
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this.simulatePBD(dt, gravity);
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else
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this.simulateAnalytic(dt, gravity);
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}
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simulatePBD(dt, gravity)
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{
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var p = this;
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for (var i = 1; i < p.masses.length; i++) {
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p.vel[i].y += dt * scene.gravity;
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p.prevPos[i].x = p.pos[i].x;
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p.prevPos[i].y = p.pos[i].y;
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p.pos[i].x += p.vel[i].x * dt;
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p.pos[i].y += p.vel[i].y * dt;
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}
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for (var i = 1; i < p.masses.length; i++) {
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var dx = p.pos[i].x - p.pos[i-1].x;
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var dy = p.pos[i].y - p.pos[i-1].y;
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var d = Math.sqrt(dx * dx + dy * dy);
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var w0 = p.masses[i - 1] > 0.0 ? 1.0 / p.masses[i - 1] : 0.0;
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var w1 = p.masses[i] > 0.0 ? 1.0 / p.masses[i] : 0.0;
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var corr = (p.lengths[i] - d) / d / (w0 + w1);
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p.pos[i - 1].x -= w0 * corr * dx;
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p.pos[i - 1].y -= w0 * corr * dy;
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p.pos[i].x += w1 * corr * dx;
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p.pos[i].y += w1 * corr * dy;
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}
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for (var i = 1; i < p.masses.length; i++) {
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p.vel[i].x = (p.pos[i].x - p.prevPos[i].x) / dt;
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p.vel[i].y = (p.pos[i].y - p.prevPos[i].y) / dt;
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}
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}
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simulateAnalytic(dt, gravity)
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{
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var g = -gravity;
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var m1 = this.masses[1];
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var m2 = this.masses[2];
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var m3 = this.masses[3];
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var l1 = this.lengths[1];
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var l2 = this.lengths[2];
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var l3 = this.lengths[3];
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var t1 = this.theta[1];
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var t2 = this.theta[2];
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var t3 = this.theta[3];
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var w1 = this.omega[1];
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var w2 = this.omega[2];
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var w3 = this.omega[3];
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var b1 =
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g*l1*m1*Math.sin(t1) + g*l1*m2*Math.sin(t1)+g*l1*m3*Math.sin(t1) + m2*l1*l2*Math.sin(t1-t2)*w1*w2 +
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m3*l1*l3*Math.sin(t1-t3)*w1*w3 + m3*l1*l2*Math.sin(t1-t2)*w1*w2 +
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m2*l1*l2*Math.sin(t2-t1)*(w1-w2)*w2 +
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m3*l1*l2*Math.sin(t2-t1)*(w1-w2)*w2 +
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m3*l1*l3*Math.sin(t3-t1)*(w1-w3)*w3;
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var a11 = l1*l1*(m1+m2+m3);
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var a12 = m2*l1*l2*Math.cos(t1-t2) + m3*l1*l2*Math.cos(t1-t2);
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var a13 = m3*l1*l3*Math.cos(t1-t3);
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var b2 =
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g*l2*m2*Math.sin(t2) + g*l2*m3*Math.sin(t2) + w1*w2*l1*l2*Math.sin(t2-t1)*(m2 + m3) +
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m3*l2*l3*Math.sin(t2-t3)*w2*w3 +
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(m2 + m3)*l1*l2*Math.sin(t2-t1)*(w1-w2)*w1 +
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m3*l2*l3*Math.sin(t3-t2)*(w2-w3)*w3;
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var a21 = (m2 + m3)*l1*l2*Math.cos(t2-t1);
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var a22 = l2*l2*(m2+m3);
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var a23 = m3*l2*l3*Math.cos(t2-t3);
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var b3 =
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m3*g*l3*Math.sin(t3) - m3*l2*l3*Math.sin(t2-t3)*w2*w3 - m3*l1*l3*Math.sin(t1-t3)*w1*w3 +
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m3*l1*l3*Math.sin(t3-t1)*(w1-w3)*w1 +
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m3*l2*l3*Math.sin(t3-t2)*(w2-w3)*w2;
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var a31 = m3*l1*l3*Math.cos(t1-t3);
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var a32 = m3*l2*l3*Math.cos(t2-t3);
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var a33 = m3*l3*l3;
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b1 = -b1;
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b2 = -b2;
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b3 = -b3;
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var det = a11 * (a22 * a33 - a23 * a32) + a21 * (a32 * a13 - a33 * a12) + a31 * (a12 * a23 - a13 * a22);
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if (det == 0.0)
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return;
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var a1 = b1 * (a22 * a33 - a23 * a32) + b2 * (a32 * a13 - a33 * a12) + b3 * (a12 * a23 - a13 * a22);
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var a2 = b1 * (a23 * a31 - a21 * a33) + b2 * (a33 * a11 - a31 * a13) + b3 * (a13 * a21 - a11 * a23);
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var a3 = b1 * (a21 * a32 - a22 * a31) + b2 * (a31 * a12 - a32 * a11) + b3 * (a11 * a22 - a12 * a21);
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a1 /= det;
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a2 /= det;
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a3 /= det;
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this.omega[1] += a1 * dt;
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this.omega[2] += a2 * dt;
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this.omega[3] += a3 * dt;
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this.theta[1] += this.omega[1] * dt;
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this.theta[2] += this.omega[2] * dt;
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this.theta[3] += this.omega[3] * dt;
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var x = 0.0, y = 0.0;
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for (var i = 1; i < this.masses.length; i++) {
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x += this.lengths[i] * Math.sin(this.theta[i]);
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y += this.lengths[i] * -Math.cos(this.theta[i]);
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this.pos[i].x = x;
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this.pos[i].y = y;
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}
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}
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updateTrail() {
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this.trail[this.trailLast] = cX(this.pos[this.pos.length-1]);
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this.trail[this.trailLast + 1] = cY(this.pos[this.pos.length-1]);
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this.trailLast = (this.trailLast + 2) % this.trail.length;
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if (this.trailLast == this.trailFirst)
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this.trailFirst = (this.trailFirst + 2) % this.trail.length;
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}
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draw() {
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c.strokeStyle = this.color;
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c.lineWidth = 2.0;
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if (this.trailLast != this.trailFirst) {
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var i = this.trailFirst;
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c.beginPath();
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c.moveTo(this.trail[i], this.trail[i + 1]);
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i = (i + 2) % this.trail.length;
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while (i != this.trailLast) {
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c.lineTo(this.trail[i], this.trail[i + 1]);
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i = (i + 2) % this.trail.length;
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}
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c.stroke();
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}
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var p = this;
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c.strokeStyle = "#303030";
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c.lineWidth = 10;
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c.beginPath();
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c.moveTo(cX(p.pos[0]), cY(p.pos[0]));
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for (var i = 1; i < p.masses.length; i++)
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c.lineTo(cX(p.pos[i]), cY(p.pos[i]));
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c.stroke();
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c.lineWidth = 1;
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c.fillStyle = this.color;
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for (var i = 1; i < p.masses.length; i++) {
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var r = 0.03 * Math.sqrt(p.masses[i]);
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c.beginPath();
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c.arc(
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cX(p.pos[i]), cY(p.pos[i]), cScale * r, 0.0, 2.0 * Math.PI);
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c.closePath();
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c.fill();
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}
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}
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}
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var scene = {
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gravity : -10.0,
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dt : 0.01,
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numSubSteps : 10000,
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paused : true,
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pendulumPBD : null,
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pendulumAnalytic : null
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};
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var sceneNr = 0;
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function setupScene() {
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var angles = [0.5 * Math.PI, Math.PI, Math.PI, Math.PI, Math.PI];
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var lengths = [];
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var masses = [];
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switch(sceneNr % 6) {
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case 0 : {
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lengths = [0.15, 0.15, 0.15];
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masses = [1.0, 1.0, 1.0];
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break;
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}
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case 1 : {
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lengths = [0.06, 0.15, 0.2];
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masses = [1.0, 0.5, 0.1];
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break;
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}
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case 2 : {
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lengths = [0.15, 0.15, 0.15];
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masses = [1.0, 0.01, 1.0];
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break;
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}
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case 3 : {
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lengths = [0.15, 0.15, 0.15];
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masses = [0.01, 1.0, 0.01];
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break;
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}
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case 4 : {
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lengths = [0.2, 0.133, 0.04];
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masses = [0.3, 0.3, 0.3];
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break;
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}
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case 5 : {
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lengths = [0.1, 0.12, 0.1, 0.15, 0.05];
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masses = [0.2, 0.6, 0.4, 0.3, 0.2];
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break;
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}
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}
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scene.pendulumAnalytic = null;
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scene.pendulumPBD = new Pendulum(true, "#FF3030", masses, lengths, angles);
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if (masses.length <= 3)
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scene.pendulumAnalytic = new Pendulum(false, "#00FF00", masses, lengths, angles);
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scene.paused = true;
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sceneNr++;
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}
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function draw() {
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c.fillStyle = "#000000";
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c.fillRect(0, 0, canvas.width, canvas.height);
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if (scene.pendulumPBD)
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scene.pendulumPBD.draw();
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if (scene.numSubSteps >= 100) {
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if (scene.pendulumAnalytic)
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scene.pendulumAnalytic.draw();
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}
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}
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function simulate() {
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if (scene.paused)
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return;
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var sdt = scene.dt / scene.numSubSteps;
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var trailGap = scene.numSubSteps / 10;
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for (var step = 0; step < scene.numSubSteps; step++) {
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if (scene.pendulumPBD) {
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scene.pendulumPBD.simulate(sdt, scene.gravity);
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if (step % trailGap == 0)
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scene.pendulumPBD.updateTrail();
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}
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if (scene.pendulumAnalytic) {
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scene.pendulumAnalytic.simulate(sdt, scene.gravity);
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if (step % trailGap == 0)
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scene.pendulumAnalytic.updateTrail();
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}
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}
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}
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document.getElementById("stepsSlider").oninput = function() {
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var steps = [1, 5, 10, 100, 1000, 10000];
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scene.numSubSteps = steps[Number(this.value)];
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document.getElementById("steps").innerHTML = scene.numSubSteps.toString();
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}
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document.addEventListener("keydown", event => {
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if (event.isComposing || event.keyCode === 229)
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return;
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if (event.key == 's')
|
||||||
|
step();
|
||||||
|
});
|
||||||
|
|
||||||
|
function run() {
|
||||||
|
scene.paused = false;
|
||||||
|
}
|
||||||
|
|
||||||
|
function step() {
|
||||||
|
scene.paused = false;
|
||||||
|
simulate();
|
||||||
|
scene.paused = true;
|
||||||
|
}
|
||||||
|
|
||||||
|
function update() {
|
||||||
|
simulate();
|
||||||
|
draw();
|
||||||
|
requestAnimationFrame(update);
|
||||||
|
}
|
||||||
|
setupScene();
|
||||||
|
update();
|
||||||
|
|
||||||
|
</script>
|
||||||
|
</body>
|
||||||
|
</html>
|
||||||
126
06-pendulumShort.html
Normal file
126
06-pendulumShort.html
Normal file
|
|
@ -0,0 +1,126 @@
|
||||||
|
<!--
|
||||||
|
Copyright 2021 Matthias Müller - Ten Minute Physics
|
||||||
|
|
||||||
|
Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:
|
||||||
|
|
||||||
|
The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
|
||||||
|
|
||||||
|
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
|
||||||
|
-->
|
||||||
|
|
||||||
|
<!DOCTYPE html>
|
||||||
|
<html>
|
||||||
|
<body>
|
||||||
|
<canvas id = "myCanvas"></canvas>
|
||||||
|
<script>
|
||||||
|
var lengths = [0.2, 0.2, 0.2];
|
||||||
|
var masses = [1.0, 0.5, 0.3];
|
||||||
|
var angles = [0.5 * Math.PI, Math.PI, Math.PI];
|
||||||
|
|
||||||
|
var canvas = document.getElementById("myCanvas");
|
||||||
|
var c = canvas.getContext("2d");
|
||||||
|
canvas.width = window.innerWidth - 20;
|
||||||
|
canvas.height = window.innerHeight - 20;
|
||||||
|
var simMinWidth = 1.0;
|
||||||
|
var cScale = Math.min(canvas.width, canvas.height) / simMinWidth;
|
||||||
|
|
||||||
|
function cX(pos) { return canvas.width / 2 + pos.x * cScale; }
|
||||||
|
function cY(pos) { return 0.4 * canvas.height - pos.y * cScale; }
|
||||||
|
|
||||||
|
class Pendulum {
|
||||||
|
constructor(masses, lengths, angles) {
|
||||||
|
this.masses = [0.0];
|
||||||
|
this.lengths = [0.0];
|
||||||
|
this.pos = [{x:0.0, y:0.0}];
|
||||||
|
this.prevPos = [{x:0.0, y:0.0}];
|
||||||
|
this.vel = [{x:0.0, y:0.0}];
|
||||||
|
var x = 0.0, y = 0.0;
|
||||||
|
for (var i = 0; i < masses.length; i++) {
|
||||||
|
this.masses.push(masses[i]);
|
||||||
|
this.lengths.push(lengths[i]);
|
||||||
|
x += lengths[i] * Math.sin(angles[i]);
|
||||||
|
y += lengths[i] * -Math.cos(angles[i]);
|
||||||
|
this.pos.push({ x:x, y:y});
|
||||||
|
this.prevPos.push({ x:x, y:y});
|
||||||
|
this.vel.push({x:0, y:0});
|
||||||
|
}
|
||||||
|
}
|
||||||
|
simulate(dt, gravity)
|
||||||
|
{
|
||||||
|
var p = this;
|
||||||
|
for (var i = 1; i < p.masses.length; i++) {
|
||||||
|
p.vel[i].y += dt * scene.gravity;
|
||||||
|
p.prevPos[i].x = p.pos[i].x;
|
||||||
|
p.prevPos[i].y = p.pos[i].y;
|
||||||
|
p.pos[i].x += p.vel[i].x * dt;
|
||||||
|
p.pos[i].y += p.vel[i].y * dt;
|
||||||
|
}
|
||||||
|
for (var i = 1; i < p.masses.length; i++) {
|
||||||
|
var dx = p.pos[i].x - p.pos[i-1].x;
|
||||||
|
var dy = p.pos[i].y - p.pos[i-1].y;
|
||||||
|
var d = Math.sqrt(dx * dx + dy * dy);
|
||||||
|
var w0 = p.masses[i - 1] > 0.0 ? 1.0 / p.masses[i - 1] : 0.0;
|
||||||
|
var w1 = p.masses[i] > 0.0 ? 1.0 / p.masses[i] : 0.0;
|
||||||
|
var corr = (p.lengths[i] - d) / d / (w0 + w1);
|
||||||
|
p.pos[i - 1].x -= w0 * corr * dx;
|
||||||
|
p.pos[i - 1].y -= w0 * corr * dy;
|
||||||
|
p.pos[i].x += w1 * corr * dx;
|
||||||
|
p.pos[i].y += w1 * corr * dy;
|
||||||
|
}
|
||||||
|
for (var i = 1; i < p.masses.length; i++) {
|
||||||
|
p.vel[i].x = (p.pos[i].x - p.prevPos[i].x) / dt;
|
||||||
|
p.vel[i].y = (p.pos[i].y - p.prevPos[i].y) / dt;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
draw() {
|
||||||
|
var p = this;
|
||||||
|
c.strokeStyle = "#303030";
|
||||||
|
c.lineWidth = 10;
|
||||||
|
c.beginPath();
|
||||||
|
c.moveTo(cX(p.pos[0]), cY(p.pos[0]));
|
||||||
|
for (var i = 1; i < p.masses.length; i++)
|
||||||
|
c.lineTo(cX(p.pos[i]), cY(p.pos[i]));
|
||||||
|
c.stroke();
|
||||||
|
c.lineWidth = 1;
|
||||||
|
|
||||||
|
c.fillStyle = "#FF0000";
|
||||||
|
for (var i = 1; i < p.masses.length; i++) {
|
||||||
|
var r = 0.05 * Math.sqrt(p.masses[i]);
|
||||||
|
c.beginPath();
|
||||||
|
c.arc(
|
||||||
|
cX(p.pos[i]), cY(p.pos[i]), cScale * r, 0.0, 2.0 * Math.PI);
|
||||||
|
c.closePath();
|
||||||
|
c.fill();
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
var scene = {
|
||||||
|
gravity : -10.0,
|
||||||
|
dt : 0.01,
|
||||||
|
numSubSteps : 100,
|
||||||
|
pendulum : new Pendulum(masses, lengths, angles)
|
||||||
|
};
|
||||||
|
|
||||||
|
function draw() {
|
||||||
|
c.fillStyle = "#000000";
|
||||||
|
c.fillRect(0, 0, canvas.width, canvas.height);
|
||||||
|
scene.pendulum.draw();
|
||||||
|
}
|
||||||
|
|
||||||
|
function simulate() {
|
||||||
|
var sdt = scene.dt / scene.numSubSteps;
|
||||||
|
for (var step = 0; step < scene.numSubSteps; step++)
|
||||||
|
scene.pendulum.simulate(sdt, scene.gravity);
|
||||||
|
}
|
||||||
|
|
||||||
|
function update() {
|
||||||
|
simulate();
|
||||||
|
draw();
|
||||||
|
requestAnimationFrame(update);
|
||||||
|
}
|
||||||
|
|
||||||
|
update();
|
||||||
|
</script>
|
||||||
|
</body>
|
||||||
|
</html>
|
||||||
Loading…
Reference in a new issue