Energy level structure of chaotic motion in bouncing ball system

We report our experimental and numerical results on the chaotic dynamics of a ball bouncing on a vertically vibrating plate. It is demonstrated that if the trajectories between collisions are classified according to the rescaled flight time, the chaotic attractor for the bouncing motion of the ball degrades into a regular structure composed of discrete energy levels in the phase space, and the motion states corresponding to these trajectories evolve into separate "microstates"populated on these levels. The probabilities of level transitions and the selection rules for the transitions are discussed. Then, the probability distribution of the energy dissipated during each collision is analyzed. It is found that there are discrete dissipation peaks in the energy dissipation spectrum. The origination of these dissipation peaks is analyzed from the perspective of level transitions. (C) 2021 Elsevier B.V. All rights reserved.