The dynamics of a bouncing ball with a sinusoidally vibrating table revisited |
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Authors: | Albert C. J. Luo Ray P. S. Han |
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Affiliation: | (1) Department of Mechanical & Industrial Engineering, University of Manitoba, R3T 2N2 Winnipeg, Manitoba, Canada |
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Abstract: | 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 constructured 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 Poincaré 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. |
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Keywords: | Bouncing ball vibrating table stability and bifurcation period-1 motion |
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