Circular gravitational billiards

Surface of section (or Poincaré map) for the a circular gravitational billiard with low energy and soft sphere interaction.

The Poincaré map is acquired by mapping the y-position and its momentum each time the sphere passes x = 0. This is done for various initial conditions with the same energy. The resulting map shows regular trajectories (closed orbits) and some seemingly random and chaotic motion (irregular orbits).

The background canvas displays both the (y,py)-phase space with highlighted section (top) and the (x,y)-trajectory (bottom).

0:00 intro
0:23 Poincaré map (selected regular orbits)
0:31 regular
1:09 irregular (chaotic 🔥)
1:24 regular

The simulations were performed using high order explicit symplectic integrators and rendered in real time.

🎵 "Moving ice" (extended version), original by "LHS" | not affiliated with/endorsed by.

[PendragonDaGreat]

Thank you for labelling the axes on the graph, ite really does help figure out what is being mapped.