Rolling ball on rotating conical turntable

Simulation of balls rolling without slipping the surface of rotating turntables and cones. The simulations demonstrate counter-intuitive motions resulting from conservation of angular momentum and the implications of the moment of inertia of two bodies.

The system is nonholonomic, and while integrals do exist at least for some of the demonstrated cases, the numerical integration was performed using the ordinary differential equations without a canonical Hamiltonian form. In all cases, the orientation of the ball is simulated with separate/decoupled equations as the Lagrangian depends on the angular velocities of the ball but not its orientation.

The simulation was performed using high order explicit symplectic integrators and was rendered in real time.

🎵 "ARYX" by "Karsten Koch" | not affiliated with/endorsed by.

[Zymplectic]

Apparently nobody bothered making a simulation of these systems with more than 5 fps, so here we go.

[BashirAlHassoun]

Cool video! Can you please upload the simulation?

[nzuckman]

The world's longest game of roulette

[cgames]

What is the music? It sounds like seytoniks (artist) to me, not sure if I got the name right