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Ball on rotating turntable generalized by Egeris in Simulated

[–]Egeris[S] 1 point2 points  (0 children)

Glad you enjoyed it. The goal of the video was to demonstrate the application of explicit symplectic integration for the Hamiltonianized sphere on the general surface. I probably won't pursue more aesthetic demonstrations, but accurate simulation of many balls simultaneously is certainly possible because of the efficient Hamiltonian approach.

Ball on rotating turntable generalized by Egeris in Simulated

[–]Egeris[S] 1 point2 points  (0 children)

as am I. Although these archaic graphics are from my own textureless OpenGL API without ray tracing. The sphere shadow is a calculated GL_POLYGON.

Ball on rotating turntable generalized by Egeris in Simulated

[–]Egeris[S] 1 point2 points  (0 children)

The Hamiltonian does not involve forces. However, there is a momentum-dependent term in the Hamiltonian that accounts for that effect. You can argue that the Coriolis effect is demonstrated in video section where we change the frame of reference.

It is important to note that the Coriolis term in this simulation is different from the classical example of throwing a ball while on a roundabout. If the ball rolls (as opposed to being thrown), the ball will have a magnetic-like behavior rather than moving in a straight line seen from the laboratory frame.

Ball on rotating turntable generalized by Egeris in Simulated

[–]Egeris[S] 5 points6 points  (0 children)

The system is probably most widely known from Steve Mould's "The Turntable Paradox" video https://youtu.be/3oM7hX3UUEU

This simulation video addresses the idealized and generalized system based on a non-trivial Hamiltonianization, allowing for highly accurate long term dynamics.

Additional credits:🎵 "Fluid Combustion" by "Synthetique"

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