Chaotic Swinging Sticks - Cleve Moler on Mathematics and Computing
 

[URL="https://swingingsticks.com"]The Swinging Sticks[/URL] is a kinetic sculpture that exhibits chaotic motion. The device became very popular after it upstaged Tony Stark in [URL="https://www.google.com/search?q=youtube+swinging+sticks+iron+man#fpstate=ive&vld=cid:6a6186e3,vid:sbbjhNLiL3c,st:0"]Iron Man 2[/URL]. My daughter Carolyn gave me a desktop version of Swinging Sticks for Christmas. I immediately set out to simulate it.

[IMG]http://blogs.mathworks.com/cleve/files/sculpture.png[/IMG]

[B]Contents[/B]
[LIST][*][URL="https://www.labfans.com/bbs/#a9143ab6-8f3f-482e-92ee-35cf3f9190de"]Chaotic Motion[/URL][*][URL="https://www.labfans.com/bbs/#bf97f3ad-e2a5-4421-9892-a8466b18022a"]Swinging Sticks[/URL][*][URL="https://www.labfans.com/bbs/#3862e132-f69e-4702-85b6-6aeeb1406839"]Sculpture[/URL][*][URL="https://www.labfans.com/bbs/#dd331fb2-a5f9-42c6-a538-5b2cb8c9b486"]Code[/URL][/LIST][B]Chaotic Motion[/B]

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, [URL="https://blogs.mathworks.com/cleve/2016/10/31/introducing-cleves-laboratory"]swinger[/URL], and a movie is available here [URL="https://blogs.mathworks.com/cleve/files/swinger.mp4"]pendulum movie[/URL].

[B]Swinging Sticks[/B]

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 [URL="https://blogs.mathworks.com/cleve/files/swinging_sticks.m"]this code[/URL] and run it in your own MATLAB. Otherwise, here in a short slow-motion animated GIF.

[IMG]http://blogs.mathworks.com/cleve/files/sticks_gif.gif[/IMG]

And, here is a longer [URL="https://blogs.mathworks.com/cleve/files/sticks.mp4"]Swinging Sticks Video[/URL].

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

[IMG]http://blogs.mathworks.com/cleve/files/chaos.png[/IMG]

[B]Sculpture[/B]

Swinging Sticks sculptures are available in various sizes and colors. [URL="https://swingingsticks.com"]The Swinging Sticks[/URL].

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 [URL="https://www.youtube.com/watch?v=PWg6TG2bkFU"]YouTube video[/URL] by Wayne Schmidt describes the controller.

[B]Code[/B]

[URL]https://blogs.mathworks.com/cleve/files/swinging_sticks.m[/URL]

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