the sublime spherical double pendulum

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.

double spherical pendulum: side view

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…

double spherical pendulum; from below

ah… that’s a nice double pendulum!

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