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<html>
<head>
<title>JSXGraph example</title>
<link rel="stylesheet" type="text/css" href="../distrib/jsxgraph.css" />
<script type="text/javascript" src="/javascript/prototype/prototype.js"></script>
<script type="text/javascript" src="../distrib/jsxgraphcore.js"></script>
<script type="text/javascript" src="../src/Centroid.js"></script>
<script type="text/javascript" src="../src/Triangle.js"></script>
</head>
<body>
<h2>Solving ODE numerically with explicit Runge-Kutta-methods</h2>
<div style="width:800px">
<div id="jxgbox" class="jxgbox" style="width:600px; height:600px; float:left;"></div>
</div>
<script type="text/javascript">
/* <![CDATA[ */
(function () {
var board = JXG.JSXGraph.initBoard('jxgbox', {boundingbox: [-1.5, 1.5, 1.5, -1.5], axis: false, grid: false}),
mu = 1.0/81.45,
apolloPath, moonPath,
moon, apollo, earth,
ode = function () {
var I = [17.066, 0],
x0 = [0.994, 0, 0, -2.0015851063790825],
N = 10000,
data, dataX, dataY, i,
f = function(t, x) {
var m = 1.0/81.45,
D1 = Math.sqrt(Math.pow((x[0]+m)*(x[0]+m)+x[2]*x[2],3)),
D2 = Math.sqrt(Math.pow((x[0]-(1-m))*(x[0]-(1-m))+x[2]*x[2],3)),
y = [];
y[0] = x[1];
y[1] = x[0]+2*x[3]-(1-m)*(x[0]+m)/D1-m*(x[0]-(1-m))/D2;
y[2] = x[3];
y[3] = x[2]-2*x[1]-(1-m)*x[2]/D1-m*x[2]/D2;
return y;
};
data = JXG.Math.Numerics.rungeKutta('rk4', x0, I, N, f);
dataX = [];
dataY = [];
for(i = 0; i < data.length; i++) {
dataX[i] = data[i][0];
dataY[i] = data[i][2];
}
return [dataX, dataY];
},
circle = function (radius, points) {
var dataX = [], dataY = [], i;
for (i = 0; i < points; i++) {
dataX[i] = radius*Math.cos(i/(points-1)*2*Math.PI);
dataY[i] = -radius*Math.sin(i/(points-1)*2*Math.PI);
}
return [dataX, dataY];
};
earth = board.create('point', [0, 0], {
withLabel: false,
strokeColor: '#4096EE',
fillColor: '#4096EE',
size: 40
});
apolloPath = board.createElement('curve', ode(), {
strokeColor: 'red',
strokeWidth: 2,
visible: false
});
moonPath = board.create('curve', circle(1-mu, apolloPath.dataX.length), {
strokeColor: 'green',
strokeWidth: 2,
visible: false
});
moon = board.create('point', [1, 0], {
withLabel: false,
strokeColor: 'gray',
fillColor: 'gray',
size: 10
});
apollo = board.create('point', [1, 0], {
withLabel: false,
strokeColor: 'white',
fillColor: 'white',
size: 2,
face: '<>'
});
moon.moveAlong(function (i) {
return [moonPath.dataX[i%moonPath.dataX.length], moonPath.dataY[i%moonPath.dataY.length]];
}, 2000);
apollo.moveAlong(function (i) {
return [apolloPath.dataX[i%apolloPath.dataX.length], apolloPath.dataY[i%apolloPath.dataY.length]];
}, 2000);
})();
/* ]]> */
</script>
<a href="#" onclick="createCurve();">Solve example ODE</a><br />
<div id="debug" style="display:block;"></div>
</body>
</html>
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