The horizontal stability of a ball bouncing upon a vertically vibrated concave surfaceH. S. Wright, M. R. Swift and P. J. King
School of Physics and Astronomy, University of Nottingham - Nottingham, NG7 2RD, UK
received 10 May 2007; accepted in final form 6 November 2007; published January 2008
published online 3 December 2007
In experiments a ball will not bounce repeatedly in the same place upon a vertically vibrating horizontal surface due to imperfections in the ball and the surface. Consequently, a concave surface is often used to restrain the horizontal movement of the ball while measurements are made of its vertical motion. Here we use two numerical-simulation models to study the horizontal motion of an inelastic sphere bouncing chaotically under gravity upon a vertically vibrated parabolic surface. Both models predict the same generic features. For almost flat surfaces the ball makes wandering horizontal excursions and as the surface curvature is increased the horizontal motion of the ball becomes more and more constrained. However, the horizontal motion may exhibit intermittent, abrupt and erratic bursts of very large amplitude. These bursts occur with a probability which increases extremely rapidly with surface curvature such that there is an effective threshold curvature for their observation within a finite sequence of bounces. We study the behaviour of this intermittency as a function of the vibration amplitude, of the surface curvature and of the normal coefficient of restitution.
45.05.+x - General theory of classical mechanics of discrete systems.
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