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vtvt_demo_8-1.html
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vtvt_demo_8-1.html
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<!DOCTYPE html>
<html lang="en-CA">
<head>
<title>vtvt demo</title>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<link rel="stylesheet" href="vtvt_demo_styles.css">
<script type="text/javascript" src="vtvt.js"></script>
<style>
.slidercontainer {
display: block;
position: relative;
margin-top: 0rem;
margin-bottom: 0rem;
text-align: center;
}
@media screen and (max-width: 42em) {
.slider {
width: 80vmin; } }
@media screen and (min-width: 42em) and (max-width: 64em) {
.slider {
width: 60vmin; } }
@media screen and (min-width: 64em) {
.slider {
width: 40vmin; } }
</style>
</head>
<body>
<h3>Demo canvas #8</h3>
<p>This demo visualizes numerical solutions of the pendulum equation by 3blue1brown: https://www.youtube.com/watch?v=p_di4Zn4wz4 (14:28).</p>
<p>Instructions:</p>
<p>Position the starting point in the phase space (angle θ, angular velocity θ′) by dragging it. The starting pendulum position (L sin θ, -L cos θ) will be adjusted automatically based on the position in the phase space. Click "animate" to see the solution (2,000 iterations). Please note the current version of vtvt doesn't disable the animation control button while an animation sequence is being played, so it's best not to press the button again until the current animation sequence is over.</p>
<p>The iteration step is 0.005 by default, and can be adjusted in your browser's console by changing variable `step`. The length of the pendulum and the dampening coefficient can be changed with the sliders underneath the canvas. </p>
<p>Please note this demo may run a bit "heavy" on older mobile devices.</p>
<p><button id='animation_trigger'>Press to animate </button></p>
<div class="canvas-wrapper">
<canvas id='vector_canvas' class="canvas-wrapped"></canvas>
</div>
<div class="slidercontainer"><div style=“display:inline-block;”>
<label for="muSlider"">μ: </label>
<input type="range" id="muSlider" min="0" max="2" value="1" step="0.1" class="slider">
<label for="muSlider" id="muValue" ">1.0</label>
</div></div>
<div class="slidercontainer"><div style=“display:inline-block;”></div>
<label for="lSlider"">L: </label>
<input type="range" id="lSlider" min="0.5" max="9.9" value="4" step="0.1" class="slider">
<label for="lSlider" id="lValue" ">4.0</label>
</div></div>
<script>
//*************************************************************************************************
// Demo canvas #8
// Pendulum equations by 3blue1brown https://www.youtube.com/watch?v=p_di4Zn4wz4 (14:28)
var g = 10;
var step = 0.005; // numerical step length
// create sliders and variables for mu and l
var muSlider = document.getElementById("muSlider");
var muValue = document.getElementById("muValue");
var mu = muSlider.value;
var lSlider = document.getElementById("lSlider");
var lValue = document.getElementById("lValue");
var l = lSlider.value;
// Process slider changes
muSlider.oninput = function() {
mu = this.value;
muValue.innerHTML=Number.parseFloat(mu).toFixed(1);
scene.render();
}
lSlider.oninput = function() {
l = this.value;
lValue.innerHTML=Number.parseFloat(l).toFixed(1);
scene.render();
}
// initialize the scene
var scene = new vtvt({canvas_id: "vector_canvas", grid_res: 16, circle_rad: 0.8, point_rad: 0.07, show_matrix: false, show_eig: false, frame_duration: 0, anim_trigger_id: "animation_trigger"});
// number of starting points
var numPoints = 3;
var colours=['60,50,230','40,170,40','200,50,50'];
// add points
for (let i = 0; i < numPoints; i+=1) {
// add point
scene.addVector({
coords: [Math.random()*16-8,Math.random()*16-8],
c: colours[i],
draggable: true,
kind: 'point',
visible: true,
label: ['(θ',String.fromCharCode(i+48+8272),', ', 'θ\′', String.fromCharCode(i+48+8272), ')'].join('')
});
}
for (let i = 0; i < numPoints; i+=1) {
scene.addVector({
c: colours[i],
draggable: false,
kind: 'custom',
draw_arrow: false,
draw_point: true,
draw_stem: true,
draw_line: false,
visible: true,
label: ['L(sin θ', String.fromCharCode(i+48+8272), ', ', '-cos θ', String.fromCharCode(i+48+8272), ')'].join(''),
map_coords: function () {
return {
mapX: l*Math.sin(scene.vectors[i].coord_x),
mapY: -l*Math.cos(scene.vectors[i].coord_x)
};
}
});
}
// add axis labels using invisible vectors (a hack)
scene.addVector({
coords:[7.5,0.01],
c:[80,80,80],
draggable: false,
kind: 'custom',
draw_arrow: false,
draw_point: false,
draw_stem: false,
draw_line: false,
visible: true,
label: 'θ'
});
scene.addVector({
coords:[0.01,7.5],
c:[80,80,80],
draggable: false,
kind: 'custom',
draw_arrow: false,
draw_point: false,
draw_stem: false,
draw_line: false,
visible: true,
label: 'θ\′'
});
//scene.addVector( {coords: [-5, 5], c: '0,30,255', draggable: true, kind: 'point', label: 'START' } );
// create vector field vectors at [j,k] whose coords and colour update based on mu and l
for (let j = -8; j < 9; j+=0.5) {
for (let k = -8; k < 9; k+=0.5) {
// coordinate map_coords function
let vec_map = function() {
let x = k;
let y = -mu*k - g/l*Math.sin(j);
let norm = Math.sqrt(x*x+y*y);
x = x/norm/2;
y = y/norm/2;
return {mapX: x, mapY: y} ;
}
// determine colour based on norm (won't update itself based on mu and l!)
let colour = function() {
let max_norm = Math.sqrt(scene.grid_res*scene.grid_res/4 + Math.pow(mu*scene.grid_res/2 + g/l,2));
let x = k;
let y = -mu*k - g/l*Math.sin(j);
let norm = Math.sqrt(x*x+y*y);
let red = 155+100*norm/max_norm;
let green = 255-120*Math.abs(0.5-norm/max_norm);
let blue = 255-100*norm/max_norm;
return `${Math.round(red)}, ${Math.round(green)}, ${Math.round(blue)}`;
}
scene.addVector({origin: [j,k], c:'220,220,220', kind: 'vector', map_coords: vec_map, map_col: colour });
}
}
// add animation vectors
let tempArr=[];
for (let i = 0; i < numPoints; i+=1) {
tempArr.push( {
c: colours[i],
kind: 'point',
map_coords:function() {
return {mapX: scene.vectors[i].coord_x,
mapY: scene.vectors[i].coord_y };
}
}
);
}
for (let i = 0; i < numPoints; i+=1) {
tempArr.push({
c: colours[i],
draggable: false,
kind: 'custom',
draw_arrow: false,
draw_point: true,
draw_stem: true,
draw_line: false,
visible: true,
label: ['L(sin θ', String.fromCharCode(i+48+8272), ', ', '-cos θ', String.fromCharCode(i+48+8272), ')'].join(''),
map_coords: function () {
return {mapX: l*Math.sin(scene.vectors[i].coord_x),
mapY: -l*Math.cos(scene.vectors[i].coord_x) };
}
}
);
}
scene.addAnimationFrame(tempArr);
for (let i = 1; i<2000; i++) {
let tempArr=[];
for (let j = 0; j < numPoints; j+=1) {
tempArr.push( {
c: colours[j],
kind: 'point',
map_coords: function() {
let x = scene.vectors_animated[i-1][j].coord_x;
let y = scene.vectors_animated[i-1][j].coord_y;
return {mapX: x + y*step,
mapY: y - (mu*y + g/l*Math.sin(x))*step }
}
} );
}
for (let j = 0; j < numPoints; j+=1) {
tempArr.push({
c: colours[j],
draggable: false,
kind: 'custom',
draw_arrow: false,
draw_point: true,
draw_stem: true,
draw_line: false,
visible: true,
label: ['L(sin θ', String.fromCharCode(j+48+8272), ', ', 'cos θ', String.fromCharCode(j+48+8272), ')'].join(''),
map_coords: function () {
let x = scene.vectors_animated[i-1][j].coord_x;
let y = scene.vectors_animated[i-1][j].coord_y;
return {mapX: l*Math.sin(x + y*step),
mapY: -l*Math.cos(x + y*step) };
}
} );
}
scene.addAnimationFrame(tempArr);
}
// render
scene.render();
</script>
</body>
</html>