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This is a crosspost from   Cleve’s Corner: Cleve Moler on Mathematics and Computing Cleve Moler is the author of the first MATLAB, one of the founders of MathWorks, and is currently Chief Mathematician at the company. He writes here about MATLAB, scientific computing and interesting mathematics.. See the original post here.

Chaotic Swinging Sticks

The Swinging Sticks is a kinetic sculpture that exhibits chaotic motion. The device became very popular after it upstaged Tony Stark in Iron Man 2. My daughter Carolyn gave me a desktop version of Swinging Sticks for Christmas. I immediately set out to simulate it.


Chaotic Motion

Chaotic motion appears random but isn't. Once the motion begins, the initial conditions together with Newton's law of motion, F = ma, determine subsequent behavior. There are no random forces. It may be difficult to predict positions, but they are well-determined, nonetheless.

A classic example of chaotic motion is the double pendulum. One mass at end of a massless string swings about a fixed pivot, and a second mass is attached by a massless string to the first. My simulator of the classis double pendulum is available in Cleve's Lab, swinger, and a movie is available here pendulum movie.

Swinging Sticks

The swinging sticks are similar to the double pendulum. The sticks are two rods with uniformly distributed mass, different lengths and off-center pivots. The best way to view the motion is to download this code and run it in your own MATLAB. Otherwise, here in a short slow-motion animated GIF.

And, here is a longer Swinging Sticks Video.

The motion of the shorter of the two rods is chaotic. Here are the orbits traced by the ends of the short rod.


Swinging Sticks sculptures are available in various sizes and colors. The Swinging Sticks.

Our mathematical model is of a frictionless perpetual motion machine. The real sculptures have an ingenious electromagnetic controller in the base that is claimed to run for two years on four AA batteries. Mine has been running since Christmas. An excellent YouTube video by Wayne Schmidt describes the controller.



Get the MATLAB code

Published with MATLAB® R2024a