Definition:Lissajous-Bowditch Figure
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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:
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