Newtonian versus general-relativistic prediction for the trajectory of a bouncing ball system

The dynamics of a bouncing ball undergoing repeated inelastic impact with a sinusoidally-oscillating table is studied numerically. For the ball bouncing at low speed in a weak gravitational field, we show, contrary to expectation, that the trajectories predicted by Newtonian mechanics and general-relativistic mechanics from the same parameters and initial conditions will rapidly disagree completely if the trajectories are chaotic. When the two theories predict completely different chaotic trajectories for a low-speed weak-gravity system, we expect the general-relativistic prediction is empirically correct since general relativity continues to be verified in recent high-precision experiments.