A ball dropped on a vertically vibrating table exhibits intricate dynamical behaviors including period-doubling bifurcations and chaos.If the collision between the ball and the table is completely inelastic,the motion of the ball is always periodic,and the plateaus caused by saddle-node instability and clumping structures for periodic trajectories occur in the bifurcation diagram.Here the effect of air damping on the dynamics of the ball with zero elasticity is analyzed.The air damping is treated as linear ...