A trochoid is the locus of a point at a distance from the center of a circle of
radius
rolling on a fixed line. A trochoid has parametric equations
(1)
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(2)
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If , the trochoid is known as a curtate cycloid; if
, it is a cycloid; and if
, the curve is a prolate
cycloid.
The arc length function, curvature, and tangential angle are given by
(3)
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(4)
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(5)
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where is an incomplete elliptic
integral of the second kind and
is the floor function.