The double pendulum is a simple and elegant demonstration of a complex system. A single pendulum consists of a weight that is free to rotate about a fixed axis. Pendulums have been used since the 1600s in clocks. Pendulums swing back and forth with a constant time between each swing, that depends of the length of the pendulum, making them useful in time keeping.
A double pendulum is a system in which a single pendulum has a second single pendulum attached at the end of the first. Under certain conditions, such as small oscillations, the double pendulum can be just as consistent as the single pendulum, however under more extreme cases the double pendulum can behave erratically. What is interesting about the double pendulum is that it is a system of deterministic chaos. That is, for a given starting position, you can predict where the pendulum will be at some point in the future. However, even incredibly slight variations in the starting location can lead to very different positions only a short time later.
If you haven’t already, take a look at the Stanford Complexity Group’s double pendulum video, and then try the simulation below.
See if you can recreate the behaviors in the video. Can you make the single pendulum behave in a periodic way with both weights moving in the same direction? What about if the weights are moving in different directions? What kind of chaotic behavior can you get?