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?”‘
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.
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!