ISSN:
1573-269X
Keywords:
Bouncing ball
;
vibrating table
;
stability and bifurcation
;
period-1 motion
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00114795
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