i like pendula in all forms as a way to visualize interesting dynamical systems. i’m most interest in the mathematics behind it all, but occasionally, i let my initial training in mechanical engineering get the best of me. this is one of those times.
consider what happens when you have a double-pendulum, but where the joints are spherical as opposed to planar (or “hinge”) in nature. this is really beautiful.
this can be a little difficult to visualize properly, since there is motion out of the plane of view. let’s take a look at the exacy same simulation, but from below…
ah… that’s a nice double pendulum!