Trochoid: Difference between revisions

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Line 11: Line 11:
<script language="JavaScript">
<script language="JavaScript">
  board = JXG.JSXGraph.initBoard('jsxgbox', {originX: 250, originY: 250, unitX: 25, unitY: 25});
  board = JXG.JSXGraph.initBoard('jsxgbox', {originX: 250, originY: 250, unitX: 25, unitY: 25});
board.suspendUpdate();
  board.createElement('axis', [[0,0],[1,0]]);
  board.createElement('axis', [[0,0],[1,0]]);
  board.createElement('axis', [[0,0],[0,1]]);
  board.createElement('axis', [[0,0],[0,1]]);
Line 19: Line 20:
  var c1 = board.createElement('curve', [x,y,'phi',-Math.PI*4,Math.PI*4],{strokeWidth:3});
  var c1 = board.createElement('curve', [x,y,'phi',-Math.PI*4,Math.PI*4],{strokeWidth:3});
   
   
  var X = function(phi) { return board.D(y)(phi)/(y(phi)*board.D(x)(phi)-x(phi)*board.D(y)(phi)); }
  var dualCurve = function(x,y,board) {
var Y = function(phi) { return board.D(x)(phi)/(x(phi)*board.D(y)(phi)-y(phi)*board.D(x)(phi)); }
    var X = function(phi) { return board.D(y)(phi)/(y(phi)*board.D(x)(phi)-x(phi)*board.D(y)(phi)); }
  var c2 = board.createElement('curve', [X,Y,'phi',-Math.PI*1,Math.PI*1],{strokeWidth:3, strokeColor:'red'});
    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.createElement('curve', [dual[0],dual[1],'phi',-Math.PI*1,Math.PI*1],{strokeWidth:3, strokeColor:'red'});
board.unsuspendUpdate();
</script>  
</script>  
</html>
</html>
[[Category:Examples]]

Revision as of 17:06, 5 February 2009

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

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