The Cycloid
Introduction:
The cycloid is a famous curve traced by a point on the edge of a rolling wheel.
Definition:
Geometrically, the cycloid is formed by tracing a point on the edge of a circle B of radius b that is concentric to a circle A of radius a, as circle A rolls without slipping along the x-axis. If the radius of B is less than that of A, then the cycloid is said to be curtate. If the radius of A is smaller, the cycloid is said to be prolate.
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| A curtate cycloid. | A prolate cycloid. |
Properties:
Velocity and Acceleration:
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The Tangent Vector:
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Arc Length: |
Curvature:
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