Added problems and solutions
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revolvingStick.html
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240
revolvingStick.html
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<!--
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This work is licensed under CC BY-NC-ND 4.0
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Link to license: http://creativecommons.org/licenses/by-nc-nd/4.0/
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Attribute to Russell Georgi
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-->
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<html>
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<head>
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<meta http-equiv="content-type" content="text/html; charset=UTF8">
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<title>
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Revolving Stick
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</title>
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<style>
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html, body {
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width: 100%;
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height: 100%;
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margin: 0px;
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border: 0;
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overflow: hidden;
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display: block;
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}
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canvas {
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position: absolute;
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}
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.greenSlider {
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-webkit-appearance: none;
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border-radius: 5px;
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height: 10px;
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background: #d3d3d3;
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outline: none;
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opacity: 0.7;
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-webkit-transition: .2s;
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transition: opacity .2s;
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}
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.greenSlider::-webkit-slider-thumb {
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-webkit-appearance: none;
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appearance: none;
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background: #000000;
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border-radius: 50%;
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width: 15px;
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height: 15px;
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cursor: pointer;
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}
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.greenSlider::-moz-range-thumb {
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background: #000000;
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border-radius: 50%;
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width: 15px;
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height: 15px;
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cursor: pointer;
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}
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</style>
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</head>
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<body>
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<canvas id="myCanvas" width="1" height="1" style="border:1px solid #ffffff;">
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Your browser does not support the HTML5 canvas tag.</canvas>
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<div class="slidecontainer">
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<t>Theta</t>
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<input type="range" min="0.01" max="1.57" value="0.52" step="0.01" class="greenSlider" id="wRSlider">
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</div>
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<script>
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var c = document.getElementById("myCanvas");
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var ctx = c.getContext("2d");
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c.width = window.innerWidth;
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c.height = window.innerHeight;
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//Time step
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var dt = 0.01;
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var t = 0;
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var l = 100;
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var theta = 0.52;
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var m = 1;
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var g = 98;
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var w = Math.sqrt(3 * g / (2 * l * Math.cos(theta)));
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var vectorMultiplier = 25;
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var cTwo = 0.2;
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//Relative position of canvas
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var xPos = 0;
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var yPos = 0;
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//Moves and scales canvas
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ctx.translate(ctx.canvas.width / 2, ctx.canvas.height / 2)
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ctx.scale(2, -2);
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function fnx(x, y, z)
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{
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return (x + y) / Math.SQRT2;
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}
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function fny(x, y, z)
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{
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return z + cTwo * (y - x);
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}
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wRSlider.oninput = function()
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{
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theta = parseFloat(this.value);
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w = Math.sqrt(3 * g / (2 * l * Math.cos(theta)));
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}
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function Clear(ctx)
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{
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ctx.clearRect(-c.width, -c.height, c.width * 2, c.height * 2);
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}
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function Update()
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{
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Clear(ctx);
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Draw();
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t += dt;
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setTimeout(Update, 1);
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}
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function Reset()
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{
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t = 0;
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rp = 0;
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thetap = 0;
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theta = Math.PI / 18;
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r = 100;
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}
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function Draw()
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{
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ctx.lineWidth = 1;
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ctx.strokeStyle = "#000000";
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ctx.beginPath();
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ctx.moveTo(xPos + fnx(0, 0, 0), yPos + fny(0, 0, 0));
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ctx.lineTo(
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xPos + fnx(l * Math.sin(theta) * Math.cos(t * w), - l * Math.sin(theta) * Math.sin(t * w), - l * Math.cos(theta)),
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yPos + fny(l * Math.sin(theta) * Math.cos(t * w), - l * Math.sin(theta) * Math.sin(t * w), - l * Math.cos(theta))
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);
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ctx.stroke();
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iStep = Math.PI / 100;
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ctx.lineWidth = 0.2;
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ctx.strokeStyle = "#888888";
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ctx.beginPath();
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ctx.moveTo(
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xPos + fnx(l * Math.sin(theta) * Math.cos(0), - l * Math.sin(theta) * Math.sin(0), - l * Math.cos(theta)),
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yPos + fny(l * Math.sin(theta) * Math.cos(0), - l * Math.sin(theta) * Math.sin(0), - l * Math.cos(theta))
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);
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for (i = 0; i <= Math.PI * 2; i += iStep)
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{
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ctx.lineTo(
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xPos + fnx(l * Math.sin(theta) * Math.cos(i), - l * Math.sin(theta) * Math.sin(i), - l * Math.cos(theta)),
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yPos + fny(l * Math.sin(theta) * Math.cos(i), - l * Math.sin(theta) * Math.sin(i), - l * Math.cos(theta))
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);
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}
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ctx.stroke();
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ctx.lineWidth = 1;
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ctx.strokeStyle = "#ff0000";
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vector(
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fnx(0, 0, 0),
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fny(0, 0, 0),
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fnx(0, 0, w * vectorMultiplier),
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fny(0, 0, w * vectorMultiplier),
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w * vectorMultiplier/ 8,
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"#ff0000"
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);
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ctx.scale(1, -1);
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ctx.beginPath();
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ctx.fillText("ω", fnx(0, 0, w * vectorMultiplier + 5), -fny(0, 0, w * vectorMultiplier + 5));
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ctx.fill();
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ctx.scale(1, -1);
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ctx.lineWidth = 1;
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ctx.strokeStyle = "#00ff00";
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am = m * l * l * w * Math.sin(theta) / 200;
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vector(
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fnx(0, 0, 0),
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fny(0, 0, 0),
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fnx(am * Math.cos(theta) * Math.cos(t * w), - am * Math.cos(theta) * Math.sin(t * w), am * Math.sin(theta)),
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fny(am * Math.cos(theta) * Math.cos(t * w), - am * Math.cos(theta) * Math.sin(t * w), am * Math.sin(theta)),
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am / 8,
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"#00ff00"
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);
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ctx.scale(1, -1);
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ctx.beginPath();
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ctx.fillText(
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"L",
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fnx(am * Math.cos(theta) * Math.cos(t * w), - am * Math.cos(theta) * Math.sin(t * w), am * Math.sin(theta) + 5),
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-fny(am * Math.cos(theta) * Math.cos(t * w), - am * Math.cos(theta) * Math.sin(t * w), am * Math.sin(theta) + 5)
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);
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ctx.fill();
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ctx.scale(1, -1);
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/*
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vector(
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fnx(l * Math.sin(theta) * Math.cos(t * w) / 2, - l * Math.sin(theta) * Math.sin(t * w) / 2, - l * Math.cos(theta) / 2),
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fny(l * Math.sin(theta) * Math.cos(t * w) / 2, - l * Math.sin(theta) * Math.sin(t * w) / 2, - l * Math.cos(theta) / 2),
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fnx(
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am * Math.cos(theta) * Math.cos(t * w) + l * Math.sin(theta) * Math.cos(t * w) / 2,
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-am * Math.cos(theta) * Math.sin(t * w) - l * Math.sin(theta) * Math.sin(t * w) / 2,
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am * Math.sin(theta) - l * Math.cos(theta) / 2
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),
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fny(
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am * Math.cos(theta) * Math.cos(t * w) + l * Math.sin(theta) * Math.cos(t * w) / 2,
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-am * Math.cos(theta) * Math.sin(t * w) - l * Math.sin(theta) * Math.sin(t * w) / 2,
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am * Math.sin(theta) - l * Math.cos(theta) / 2
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),
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8,
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"#00ff00"
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);
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*/
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}
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window.addEventListener('resize', function(event) {
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c.width = window.innerWidth;
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c.height = window.innerHeight;
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ctx.translate(c.width / 2, c.height / 2);
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ctx.scale(2, -2);
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}, true);
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function vector(xv, yv, xvv, yvv, va, cl)
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{
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vl = ((xvv - xv) ** 2 + Math.pow(yvv - yv, 2)) ** (1/2);
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ctx.strokeStyle = cl;
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ctx.beginPath();
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ctx.moveTo(xPos + xv, yPos + yv);
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ctx.lineTo(xPos + xvv, yPos + yvv);
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ctx.stroke();
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ctx.beginPath();
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ctx.moveTo(xPos + xvv, yPos + yvv);
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ctx.lineTo(xPos + xvv - va / vl * (xvv - xv) + va / vl / 2 * (yvv - yv), yPos + yvv - va / vl * (yvv - yv) - va / vl / 2 * (xvv - xv));
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ctx.stroke();
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ctx.beginPath();
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ctx.moveTo(xPos + xvv, yPos + yvv);
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ctx.lineTo(xPos + xvv - va / vl * (xvv - xv) - va / vl / 2 * (yvv - yv), yPos + yvv - va / vl * (yvv - yv) + va / vl / 2 * (xvv - xv));
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ctx.stroke();
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}
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Update();
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</script>
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</body>
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<p xmlns:cc="http://creativecommons.org/ns#" style="font-size: 1vw; bottom: 0px; position: absolute;">
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This work is licensed under
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<a href="http://creativecommons.org/licenses/by-nc-nd/4.0/?ref=chooser-v1" target="_blank" rel="license noopener noreferrer" style="display:inline-block;">CC BY-NC-ND 4.0<img style="height:22px!important;margin-left:3px;vertical-align:text-bottom;" src="https://mirrors.creativecommons.org/presskit/icons/cc.svg?ref=chooser-v1"><img style="height:22px!important;margin-left:3px;vertical-align:text-bottom;" src="https://mirrors.creativecommons.org/presskit/icons/by.svg?ref=chooser-v1"><img style="height:22px!important;margin-left:3px;vertical-align:text-bottom;" src="https://mirrors.creativecommons.org/presskit/icons/nc.svg?ref=chooser-v1"><img style="height:22px!important;margin-left:3px;vertical-align:text-bottom;" src="https://mirrors.creativecommons.org/presskit/icons/nd.svg?ref=chooser-v1"></a></p>
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</html>
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