Python Activity - Double Pendulum (Chaotic system)

This activity builds off of the last one, where we begin to see and use an actual Python program to simulate the motion of real objects. Last time we looked at a tossed ball that bounces. Not only did we begin to see how to insert equations that the simulation runs over and over to calculate the points where the ball goes from time step to time step, but also had animations of the bouncing ball. That program is now a template for us to use - we can change the equations we put into the program in order to simulate other objects besides a bouncing ball.

This time, we will use a simulation for a more complicated type of motion, the double pendulum. This is a pendulum hanging from a pendulum. If we tried to calculate and plot points for this system, we could not do so by hand since it is too complicated (and also a chaotic system). So this is a case where we really do need a computer to solve the motion numerically so we can find out what it does. The activity for today is here. Some years ago, a former student wrote his own simulation for this, where he simulated two double pendula hanging from a rod, so they affected each other via vibrations through the rod (called coupled double pendula). His paper is is here if you are curious.