Chaotic Wrench: Visualizing Chaos

For one of my projects in my Nonlinear Dynamics and Chaos class this semester at Olin (Spring ’14) I built and simulated a chaotic pendulum.  I was inspired by an exhibit at the Montshire Museum of Science that I saw when I was about 8 years old.  I thought it was really cool, but I remember wondering, “How do you even pronounce ‘chaotic?”‘Screen Shot 2014-05-07 at 5.20.16 PM Screen Shot 2014-05-07 at 5.16.05 PM

The exhibit has a big flywheel that you can spin, which is attached to a crank  (inside the protective glass case).  A giant crescent-wrench is dangling from the end of the crank and it swings and spins in crazy unpredictable ways.
The exhibit description says “What appears at first to be a silly spinning wrench challenges your expectations about movement.  A light spin of the handle and the foot-long wrench jumps up in the air and whirls around. But it doesn’t always go where you think it will, and sometimes it pops up when it seems it shouldn’t. Chaos theory plays a part in whether the motion of the spinning wrench can be predicted, but, predictable or not, its motion is surprising and may make you laugh.”

My own chaotic pendulum is driven by a DC gearmotor.  The pendulum itself is an 8-inch adjustable wrench that I mounted using a pressed-in bearing to minimize friction.  When the motor is plugged into an adjustable DC power supply I can adjust the crank’s rotation to anywhere between zero and 140 RPM.  Here is what it looks like!

 

 

 

 

I simulated the pendulum using a differential equation solver in Matlab.  Starting with the equations of motion (from Physics) it calculates the position, velocity, and acceleration at each point in time, given a starting position,  starting velocity, and crank speed.  Screen Shot 2014-05-07 at 5.37.11 PM

Here’s what the simulated behavior looks like!

 

 

My goal all along was to make pretty pictures of this system in motion so I placed an LED on the end of the wrench and set it up in our dark photo studio to take some long-exposure pictures!

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Simulated Trajectories

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