# Lissajous (in the works)

## Description

Lissajous is a family of curves, given by `{a*Sin[b*t+c], Sin[t]}`

with 3 parameters.

In studying nature there often arises the wave motion `a*Sin[b*t+c]`

. For example, the motion of a pendulum. Lissajous is two such motions in perpendicular directions:

{a1*Sin[b1*t+c1], a2*Sin[b2*t+c2]}

Changing the parameter by replacing t→1/b1*t then t→c2, then scale by 1/a2, we can simplify the parameters down to `{a*Sin[b*t+c], Sin[t]}`

.

## History

Studied by Nathaniel Bowditch in 1815 and Jules Antoine Lissajous (1822 – 1880).

## Formula

Parametric: `{a*Sin[b*t+c], Sin[t]}`

The parameter a stretches the curve in one direction. Parameters b and c are more interesting. The period of the curve is the least common multiple of the two components, that is, LCM[2*π/b,2*π].

## Properties

## Related Web Sites

See: Websites on Plane Curves, Plane Curves Books.

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