The Hypotrochoid
Introduction:
The hypotrochoid is similar to the epitrochoid, except that the smaller circle rolls on the inside edge of the larger one. It has as special cases the ellipse (a = 2b) and the hypocycloid (h = b). In general, it has a/b loops.
Definition:
Geometrically, the hypotrochoid is traced by a point P, attached at a distance h to the center of a small circle of radius b as it rolls along the inside edge of a larger circle of radius a.
Properties:
Velocity and Acceleration:
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The Tangent Vector:
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Arc Length: |
Curvature:
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