Rocking disk pendulum

Simulation of rocking semicircular disk (or cylinder) with an attached pendulum mounted on the disk surface. The disk is uniform solid and is rolling without slipping. The semicircular disk has 32 times greater mass than the pendulum bob.

The Hamiltonian system has two degrees of system and exhibits regular and chaotic behavior, which is depicted for various initial conditions. The motion of the pendulum bob is displayed on the back canvas to illustrate the long term behavior of the system.

The system was simulated using high order explicit symplectic integrators and was rendered in real time.

🎵 "Lackerad Keramik" by "Ghidorah" | not affiliated with/endorsed by.

[EntropicTroponin]

Excellent show of different behavioral regimes of this pendulum. Also amazing music choice with the visualizations

[benjaminlum]

I find it super interesting that a lossless system could keep the disk on one side indefinitely 0:45, and how there's a set of initial conditions that would yield a single unique non-symmetrical path without deviation 1:18 !
P.S. i just noticed that the path is open as well!

[manugiramusic]

Amusement parks need to turn this into an attraction

[HansFormerlyTraffer]

I designed and built one of these for a college art project. One difference is that I used increasing radii on the rocker... to "kick" it back into the rock. It was made of thin wood with strings. It would (depending on the weight placed on the pendulum) allow the weight to come to "rest" on the floor before returning to a swinging motion. There were times that it appeared to have lost all of its energy and rest for over 7 seconds with the weight on the floor, only to lift up off the floor and begin to swing again. It was displayed at the University where it was marveled at for months.

[leofigoboh]

Damn, I feared it would fall over. Are the inizial conditions such that it cannot fall over?

[usmanfatih]

Yo, could you share a tutorial on how the software works? and how to create custom simulations on it? thanks. Also amazing video, keep up the good work.