THE DYNAMICS OF A BOUNCING BALL WITH A SINUSOIDALLY VIBRATING TABLE REVISITED

The dynamical behavior of a bouncing ball with a sinusoidally vibratin g table is revisited in this paper. Based on the equation of motion of the ball, the mapping for period-1 motion is constructed and thereby allowing the stability and bifurcation conditions to be determined. Co mparison with Holmes's solution [1] shows that our range of stable mot ion is wider, and through numerical simulations, our stability result is observed to be more accurate. The Poincare mapping sections of the unstable period-1 motion indicate the existence of identical Smale hor seshoe structures and fractals. For a better understanding of the stab le and chaotic motions, plots of the physical motion of the bouncing b all superimposed on the vibration of the table are presented.