Simulating a Water Wave Using a Cycloid

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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 (August 2012)
Open content licensed under CC BY-NC-SA



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.

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