It Needs David to Do the Math

2017

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OK, right up front: The math of the dynamics of this sculpture escapes me. The analysis of its motion requires a higher-octane brain than mine.

 

Hence the title: I’m pretty sure that my friend, David Snyder, has the math chops to bring off the dynamic analysis. When it comes to the analysis of physical systems, David has the same kind of reputation in the tech world that Luke Skywalker has among the Jedi. Better, actually, since David’s not fictional. Plus, he has patiently listened to me carry on about kinetic sculpture mechanics for years.

 

The sculpture is based on a mechanism proposed in the mid-1800s by Pafnuty Chebyshev, a Russian mathematician. The center element of it moves back and forth in a straight line with respect to the base, quite useful in 19th century mechanics. I could do that math, and it indeed has an impressive path deviation of less than 0.25%. This sculpture adds a pendulum to the center point to give it motion. I did the math of its static balance, and could predict that its movement would not be simple harmonic motion. But the dynamics: Rotation and translation of the energy-storing pendulum, restoring forces on the pendulum varying with complicated trigonometry!

 

What to do? David is always busy. Right now he’s probably deriving an anti-gravity engine from an old iPod and some Chilean gardening tools. So I fall back on an ancient engineering maxim: “If you can’t analyze, experiment!” It works!