Lissajous and Bowditch

I was skimming through David Well's book The Penguin Dictionary of Curious and Interesting Geometry and was surprised by this entry:

Lissajous figures orBowditch curves First discussed by Nathaniel Bowditch in 1815, and later by Jules Antoine Lissajous in 1857 ...

I wrote a couple posts about Lissajous curves years ago, and recently I wrote a couple posts about Nathan Bowditch, but I didn't realize there was a connection between them.

I asked Claude to pin down Bowditch's publication to see whether the curves came up in the course of his work on navigation. Here's the answer I got.

Bowditch's paper was On the Motion of a Pendulum Suspended from Two Points," published in the Memoirs of the American Academy of Arts and Sciences (Vol. 3, Part 2) in 1815.

He studied a compound pendulum hung from two points (a Y-shaped suspension, sometimes called a Blackburn pendulum). This lets the bob swing at different frequencies in two perpendicular directions, and he worked out mathematically the curves the bob traces. Those curves are what we now call Lissajous figures. Jules Antoine Lissajous studied them independently and much more visibly in 1857, using light beams reflected off vibrating tuning forks, and his name stuck. Because of Bowditch's priority, the curves are sometimes called Bowditch curves.

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