9860

Hypotrochoid from Collinear Orbiters

This Demonstration shows the trajectory of a red point on the segment that connects two black points and that travel around two circles. The location of is fixed in terms of the ratio . The phase or offset does not change the shape of the green orbit. The angular velocity of determines the number of lobes of the green curve it lies on.

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DETAILS

The green figure is neither a rose curve nor a cycloid. Based on its algebraic form, it can be generated by a Spirograph with two solid gears. It is a hypotrochoid with 90 degree phase offset. Also, the inner product of the and coordinate of a point on the green curve vanishes if the angular velocity is an integer, that is, the integral of their product over one period is zero.
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