The dynamics of a bouncing ball with a sinusoidally vibrating table revisited

✍ Scribed by Albert C. J. Luo; Ray P. S. Han

• Publisher: Springer Netherlands
• Year: 1996
• Tongue: English
• Weight: 934 KB
• Volume: 10
• Category: Article
• ISSN: 0924-090X
• DOI: 10.1007/bf00114795

✦ Synopsis

The dynamical behavior of a bouncing ball with a sinusoidally vibrating 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. Comparison with Holmes's solution [1] shows that our range of stable motion is wider, and through numerical simulations, our stability result is observed to be more accurate. The Poincar6 mapping sections of the unstable period-1 motion indicate the existence of identical Smale horseshoe structures and fractals. For a better understanding of the stable and chaotic motions, plots of the physical motion of the bouncing ball superimposed on the vibration of the table are presented.