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Cycloid
Author

Simo K. Kivelš
Organization: Helsinki University of Technology
Department: Institute of Mathematics
URL: http://math.tkk.fi/~kivela/, http://matta.hut.fi/matta2/
Education level

College
Description

A circle is rolling along a straight line without slipping. The locus of a point on the circumference of the rolling circle is called cycloid. If the point is inside or outside of the rolling circle, the locus is called trochoid. The parametric representation of the curve is

{t-d sin(t), 1-d cos(t)},

where t is the curve parameter, d the distance of the moving point from the center of the rolling circle and the radius of the rolling circle is 1. If d=1, the curve is cycloid, otherwise trochoid.

In the following demonstration, the distance d can be changed. When the curve parameter is changed, the curve--cycloid or trochoid--is plotted.
Subjects

*Education
*Education > College
*Mathematics
Downloads

Download
cycloid.nbp (793.9 KB) - Mathematica Player Notebook