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Gravitational wedge billiards

Simulation of an elastic soft wall (or soft sphere) gravitational wedge billiards of various wedge angles and rotations. The elastic collisions between the sphere and the soft-edge billiard is based on the transition between the up(x) function and a linear spring force. The resulting potential has continuous derivatives of all orders and is compactly supported. The long-term dynamics are displayed in the canvas, depicting regular and chaotic behavior for various initial conditions. Multiple spheres are depicted demonstrating the butterfly effect associated with chaotic dynamics. It is notable that: the orthogonal wedge billiards is always integrable exhibiting no chaotic behavior regardless of rotation. the acute wedge billiards has rich dynamical behavior of both regular and chaotic orbits. the obtuse wedge is generally chaotic (not shown in this video). 0:00 acute wedge billiards 1:04 orthogonal wedge billiards 1:50 butterfly effect (regular) 2:16 acute wedge singular trajectory 2:29 butterfly effect (chaotic) The simulation was performed using high order explicit symplectic integrators and was rendered in real time.