The Epicycloid
Introduction:
The epicycloid is like a cycloid on the circumference of a circle. It has as special cases the cardioid (when b = a in the definition below) and the nephroid (when b = a/2). It is a special case of the epitrochoid.
Definition:
Geometrically, the epicycloid is traced by a point on the radius of a small circle (of radius b) rolling on the edge of a larger circle (of radius a), as shown below.
Properties:
Velocity and Acceleration:
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The Tangent Vector:
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Arc Length: |
Curvature:
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