The chaos of a double pendulum

The above video, which is really just a chaotic system winding down, is completely fascinating to watch.

A double pendulum is constructed by connecting the pivot point of the lower pendulum to the bob of the upper pendulum. As the two pendulums swing they each impart part of their energy to the other. The result is a wildly unpredictable, and sometimes surprising, movement of the pendulum arms.  

As I dimly remember the math of a single pendulum from college physics which was rather straight forward. I shudder at what would be needed to calculate the behavior of this dual system. My guess is that it couldn't be done. Interesting how one can move from relatively simple to mind-bendingly complex so swiftly.