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Chaotic bounce on oscillating platform

Dynamics of spheres bouncing on perfectly elastic pistons mounted to an oscillating platform. The massless pistons act on the sphere with Hookean-like spring force. More precisely, the second integral of the Fabius function is used as the spring potential energy, yielding compact support and infinite differentiability. While the system is generally chaotic, certain combinations of oscillation frequencies and amplitudes exhibit regular orbits. The regular orbits are depicted as closed curves on the background canvas showing the phase space. The canvas is painted only when the oscillating platform is at origo, yielding a graphical depiction of the Poincaré map. 0:00 platform static at origo 0:21 oscillating platform (chaotic) 0:26 oscillating platform (low amplitude) 0:57 oscillating platform (high amplitude) The simulations were performed using high order explicit symplectic integrators and were rendered in real time. 🎵 "Z-TecH 1" by "Svenzzon" | CC | not affiliated with/endorsed by.