# How to explain the motion of these pendulums? [duplicate]

Got very interested recently in a video I saw running thru my feed:

Well, I got very intrigued about the physics of it and wanted to know your opinion about my guesses and how to proceed regarding them. I think that basically this mad motion is due to the fact that there's some ratio between the length of these pendulums. I spent a little time thinking and before solving the movement equations thought that maybe I couldn't use the approximation for small angles for that and MAYBE the initial motion would be related to a trasient term (indicating time interval which the system is oscillating for angles greater then 5 degrees) and then go to these repetitive patterns, for smaller angles in which the system is pretty much conservative). I thought about solving this numerically in Mathematica, plotting multiple pendulums with different lengths.

• Have you considered the equation for the period of the pendulum, $T\approx2\pi\sqrt{\frac{L}{g}}$? Nov 8, 2015 at 20:58
• Possible duplicates: physics.stackexchange.com/q/63357/2451 and links therein. Nov 8, 2015 at 21:14

Actually the pendulums swing independently, but one can consider all of them together as a Hamiltonian system. The movie illustrates the Poincare recurrence theorem. It also illustrates quasi-periodic motion on the Liouville torus in a completely integrable Hamiltonian system

• Oh, give it a rest. Nov 8, 2015 at 21:19