## Curtate Cycloid

The path traced out by a fixed point at a Radius , where is the Radius of a rolling Circle, sometimes also called a Contracted Cycloid.

 (1) (2)

The Arc Length from is
 (3)

where
 (4)

 (5)

and is a complete Elliptic Integral of the Second Kind and is a Jacobi Elliptic Function.

See also Cycloid, Prolate Cycloid

References

Cundy, H. and Rollett, A. Mathematical Models, 3rd ed. Stradbroke, England: Tarquin Pub., 1989.

Wagon, S. Mathematica in Action. New York: W. H. Freeman, pp. 46-50, 1991.

© 1996-9 Eric W. Weisstein
1999-05-25