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This Demonstration shows a curtate cycloid, a figure traced by a fixed point in the interior of a rolling circle.

Contributed by: Conrad Benulis

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A cycloid has parametric equations:

To simulate a wave, the

parameter is inverted. The actual equations used in this Demonstration are:

The term

corresponds to the wave height. Almost all Demonstrations of cycloids incorporate the rolling circle for effect. With a little effort, it was possible to show that effect (along with basic wave parameters) by tweaking the original parametric equations.

Cycloid Curves (Wolfram Demonstrations Project)

Rolling Wheel with Spoke (Wolfram Demonstrations Project)

Conrad Benulis

"Simulating a Water Wave Using a Cycloid"
http://demonstrations.wolfram.com/SimulatingAWaterWaveUsingACycloid/
Wolfram Demonstrations Project
Published: August 7, 2012

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Simulating a Water Wave Using a Cycloid

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