Trochoid: Difference between revisions
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<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]]); | ||
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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 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', [ | 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]
