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.

我们报告了关于在垂直振动板上弹跳的球的混沌动力学的实验和数值结果。证明如果根据重新缩放的飞行时间对碰撞之间的轨迹进行分类，则球弹跳运动的混沌吸引子退化为相空间中由离散能级组成的规则结构，以及与这些相空间对应的运动状态轨迹演变成独立的“微观状态”，分布在这些水平上。讨论了电平转换的概率和转换的选择规则。然后，分析每次碰撞过程中耗散的能量的概率分布。发现能量耗散谱中存在离散的耗散峰。