Difference between revisions of "Trochoid"

From JSXGraph Wiki
Jump to: navigation, search
Line 4: Line 4:
 
:<math>y = a-b\cos(\phi)</math>
 
:<math>y = a-b\cos(\phi)</math>
  
<html>
+
<jsxgraph box="jsxgbox" width="550" height="500">
<link rel="stylesheet" type="text/css" href="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraph.css" />
+
board = JXG.JSXGraph.initBoard('jsxgbox', {boundingbox:[-10,10,10,-10], axis:true});
<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script>
+
board.suspendUpdate();
<div id="jsxgbox" class="jxgbox" style="width:550px; height:500px;"></div>
+
var a = board.create('slider', [[1,-1],[8,-1],[-5,1,5]], {style:6,name:'a'});
<script language="JavaScript">
+
var b = board.create('slider', [[1,-2],[8,-2],[-5,1,5]], {style:6,name:'b'});
board = JXG.JSXGraph.initBoard('jsxgbox', {boundingbox:[-10,10,10,-10], axis:true});
+
var x = function(phi) { return a.Value()*phi-b.Value()*Math.sin(phi); }
board.suspendUpdate();
+
var y = function(phi) { return a.Value()-b.Value()*Math.cos(phi); }
var a = board.createElement('slider', [[1,-1],[8,-1],[-5,1,5]], {style:6,name:'a'});
+
var c1 = board.create('curve', [x,y,-Math.PI*4,Math.PI*4],{strokeWidth:3});
var b = board.createElement('slider', [[1,-2],[8,-2],[-5,1,5]], {style:6,name:'b'});
 
var x = function(phi) { return a.Value()*phi-b.Value()*Math.sin(phi); }
 
var y = function(phi) { return a.Value()-b.Value()*Math.cos(phi); }
 
var c1 = board.createElement('curve', [x,y,-Math.PI*4,Math.PI*4],{strokeWidth:3});
 
 
   
 
   
var dualCurve = function(x,y,board) {
+
var dualCurve = function(x,y,board) {
 
     var X = function(phi) { return board.D(y)(phi)/(y(phi)*board.D(x)(phi)-x(phi)*board.D(y)(phi)); }
 
     var X = function(phi) { return board.D(y)(phi)/(y(phi)*board.D(x)(phi)-x(phi)*board.D(y)(phi)); }
 
     var Y = function(phi) { return board.D(x)(phi)/(x(phi)*board.D(y)(phi)-y(phi)*board.D(x)(phi)); }
 
     var Y = function(phi) { return board.D(x)(phi)/(x(phi)*board.D(y)(phi)-y(phi)*board.D(x)(phi)); }
 
     return [X,Y];
 
     return [X,Y];
    }
+
}
var dual = dualCurve(x,y,board);
+
var dual = dualCurve(x,y,board);
var c2 = board.createElement('curve', [dual[0],dual[1],-Math.PI*1,Math.PI*1],{strokeWidth:3, strokeColor:'red'});
+
var c2 = board.create('curve', [dual[0],dual[1],-Math.PI*1,Math.PI*1],{strokeWidth:3, strokeColor:'red'});
board.unsuspendUpdate();
+
board.unsuspendUpdate();
</script>  
+
</jsxgraph>  
</html>
+
 
 
===References===
 
===References===
 
* [http://en.wikipedia.org/wiki/Trochoid http://en.wikipedia.org/wiki/Trochoid]
 
* [http://en.wikipedia.org/wiki/Trochoid http://en.wikipedia.org/wiki/Trochoid]
 
* [http://en.wikipedia.org/wiki/Dual_curve http://en.wikipedia.org/wiki/Dual_curve]
 
* [http://en.wikipedia.org/wiki/Dual_curve http://en.wikipedia.org/wiki/Dual_curve]
 
===The underlying JavaScript code===
 
===The underlying JavaScript code===
<source lang="xml">
+
<source lang="javascript">
<link rel="stylesheet" type="text/css" href="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraph.css" />
+
board = JXG.JSXGraph.initBoard('jsxgbox', {boundingbox:[-10,10,10,-10], axis:true});
<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script>
+
board.suspendUpdate();
<div id="jsxgbox" class="jxgbox" style="width:550px; height:500px;"></div>
+
var a = board.create('slider', [[1,-1],[8,-1],[-5,1,5]], {style:6,name:'a'});
<script language="JavaScript">
+
var b = board.create('slider', [[1,-2],[8,-2],[-5,1,5]], {style:6,name:'b'});
board = JXG.JSXGraph.initBoard('jsxgbox', {boundingbox:[-10,10,10,-10], axis:true});
+
var x = function(phi) { return a.Value()*phi-b.Value()*Math.sin(phi); }
board.suspendUpdate();
+
var y = function(phi) { return a.Value()-b.Value()*Math.cos(phi); }
var a = board.createElement('slider', [[1,-1],[8,-1],[-5,1,5]], {style:6,name:'a'});
+
var c1 = board.create('curve', [x,y,-Math.PI*4,Math.PI*4],{strokeWidth:3});
var b = board.createElement('slider', [[1,-2],[8,-2],[-5,1,5]], {style:6,name:'b'});
 
var x = function(phi) { return a.Value()*phi-b.Value()*Math.sin(phi); }
 
var y = function(phi) { return a.Value()-b.Value()*Math.cos(phi); }
 
var c1 = board.createElement('curve', [x,y,-Math.PI*4,Math.PI*4],{strokeWidth:3});
 
 
   
 
   
var dualCurve = function(x,y,board) {
+
var dualCurve = function(x,y,board) {
 
     var X = function(phi) { return board.D(y)(phi)/(y(phi)*board.D(x)(phi)-x(phi)*board.D(y)(phi)); }
 
     var X = function(phi) { return board.D(y)(phi)/(y(phi)*board.D(x)(phi)-x(phi)*board.D(y)(phi)); }
 
     var Y = function(phi) { return board.D(x)(phi)/(x(phi)*board.D(y)(phi)-y(phi)*board.D(x)(phi)); }
 
     var Y = function(phi) { return board.D(x)(phi)/(x(phi)*board.D(y)(phi)-y(phi)*board.D(x)(phi)); }
 
     return [X,Y];
 
     return [X,Y];
    }
+
}
var dual = dualCurve(x,y,board);
+
var dual = dualCurve(x,y,board);
var c2 = board.createElement('curve', [dual[0],dual[1],-Math.PI*1,Math.PI*1],{strokeWidth:3, strokeColor:'red'});
+
var c2 = board.create('curve', [dual[0],dual[1],-Math.PI*1,Math.PI*1],{strokeWidth:3, strokeColor:'red'});
board.unsuspendUpdate();
+
board.unsuspendUpdate();
</script>
 
 
</source>
 
</source>
 
[[Category:Examples]]
 
[[Category:Examples]]
 
[[Category:Curves]]
 
[[Category:Curves]]

Revision as of 08:37, 9 June 2011

The Trochoid curve (blue) and its dual curve (red). The equation of the trochoid is

[math]x = a\phi-b\sin(\phi)[/math]
[math]y = a-b\cos(\phi)[/math]

References

The underlying JavaScript code

board = JXG.JSXGraph.initBoard('jsxgbox', {boundingbox:[-10,10,10,-10], axis:true});
board.suspendUpdate();
var a = board.create('slider', [[1,-1],[8,-1],[-5,1,5]], {style:6,name:'a'});
var b = board.create('slider', [[1,-2],[8,-2],[-5,1,5]], {style:6,name:'b'});
var x = function(phi) { return a.Value()*phi-b.Value()*Math.sin(phi); }
var y = function(phi) { return a.Value()-b.Value()*Math.cos(phi); }
var c1 = board.create('curve', [x,y,-Math.PI*4,Math.PI*4],{strokeWidth:3});
 
var dualCurve = function(x,y,board) {
    var X = function(phi) { return board.D(y)(phi)/(y(phi)*board.D(x)(phi)-x(phi)*board.D(y)(phi)); }
    var Y = function(phi) { return board.D(x)(phi)/(x(phi)*board.D(y)(phi)-y(phi)*board.D(x)(phi)); }
    return [X,Y];
}
var dual = dualCurve(x,y,board);
var c2 = board.create('curve', [dual[0],dual[1],-Math.PI*1,Math.PI*1],{strokeWidth:3, strokeColor:'red'});
board.unsuspendUpdate();