Definition:Lissajous-Bowditch Figure

Definition

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.

Examples

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.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Lissajous figures
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Lissajous figures