Definition:Lissajous-Bowditch Figure

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A Lissajous-Bowditch figure is a plane curve which is the locus of a point whose coordinates move in simple harmonic motion.

The specific shape of a Lissajous-Bowditch figure depends on the relative frequencies and phases of the two motions.


Example: $\map \cos {4 t + \frac \pi 2}$ by $\map \sin {5 t}$

The Lissajous-Bowditch figure generated by the simple harmonic motions:

\(\ds x\) \(=\) \(\ds \map \cos {4 t + \frac \pi 2}\)
\(\ds y\) \(=\) \(\ds \map \sin {5 t}\)

is as follows:


Also known as

A Lissajous-Bowditch figure is also known as:

a Lissajous figure
a Bowditch curve.

Also see

  • Results about Lissajous-Bowditch figures can be found here.

Source of Name

This entry was named for Jules Antoine Lissajous and Nathaniel Bowditch.