Pendulum

From JSXGraph Wiki
Revision as of 13:21, 3 March 2021 by A WASSERMANN (talk | contribs)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
The printable version is no longer supported and may have rendering errors. Please update your browser bookmarks and please use the default browser print function instead.

Simple Pendulum with Damping

The JavaScript code

var board = JXG.JSXGraph.initBoard('jxgbox', {boundingbox: [-9, 9, 9, -12], keepaspectratio: true, false: true, grid: true}),
    p1 = board.create('point', [0.0, 0.0], {visible:false, name: 'a', size: 3}),
    c1 = board.create('circle', [p1, [0,8]], {visible:false, name: 'circle', size: 3}),
    p2 = board.create('glider', [3,-4, c1], {visible: true, name: '', size: 3}),
    grr=board.create('functiongraph', [function(t){ return -10-2*Math.cos(t/2); },-10, 10],{strokeColor: "#cccccc"}),
    p3 = board.create('point', [
                function(){return 2*Math.atan2(p2.X(),-p2.Y())},
                function(){return -10-2*Math.cos(Math.atan2(p2.X(),-p2.Y()))}], 
                {visible: true, name:'', size: 3}),
    line = board.create('line', [p1, p2], {visible:true, straightFirst: false,straightLast: false}),
    isInDragMode = false;

var gg =  board.create('slider',[[-6,6],[-3,6],[1,9.8,10]]); board.create('text',[-8,6,'gravity']);
var cc =  board.create('slider',[[3,6],[6,6],[0.1,0.5,1]]); board.create('text',[1,6,'damping']);

function startAnimation(start_theta) {
 var c = cc.Value(), g = gg.Value(), l = 10;
    p2.moveAlong(function() {
        var f = function(t, x) {
                return [x[1], -c * x[1] - g / l * (Math.sin(x[0]))];
            },
            area = [0, 200],
            numberOfEvaluations = (area[1] - area[0]) * 100,
            data = JXG.Math.Numerics.rungeKutta('heun', [start_theta, 0], area, numberOfEvaluations, f),
            duration = 20 * 1e3;
   
        return function(t) {
            if (t >= duration)
                return NaN;
            angle2=-Math.PI/2+data[Math.floor(t / duration * numberOfEvaluations)][0];
            return [p1.X()+l*Math.cos(angle2),p1.Y()+l*Math.sin(angle2)];
        };
    }());
}

function hook() {
    if(!isInDragMode) {
        if(board.mode === board.BOARD_MODE_DRAG) {
            board.stopAllAnimation();
            isInDragMode = true;
        }
    }
    if(isInDragMode) {
        if(board.mode !== board.BOARD_MODE_DRAG) {
            isInDragMode = false;
            angle=Math.atan2(p2.Y()-p1.Y(),p2.X()-p1.X())+Math.PI*1/2;
            startAnimation(angle);
        }
    }
}

board.addHook(hook);
startAnimation(-1.2);