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July  2008, 10(1): 43-72. doi: 10.3934/dcdsb.2008.10.43

On the stopping time of a bouncing ball

Anna Maria Cherubini 1, , Giorgio Metafune 1, and  Francesco Paparella 2,

1. 

Dipartimento di Matematica E. De Giorgi, Università del Salento, 73100, Lecce, Italy, Italy
2. 

Dipartimento di Matematica e Fisica "Ennio De Giorgi", Università del Salento, 73100, Lecce, Italy

Received  June 2007 Revised  January 2008 Published  April 2008

We study a simple model of a bouncing ball that takes explicitely into account the elastic deformability of the body and the energy dissipation due to internal friction. We show that this model is not subject to the problem of inelastic collapse, that is, it does not allow an infinite number of impacts in a finite time. We compute asymptotic expressions for the time of flight and for the impact velocity. We also prove that contacts with zero velocity of the lower end of the ball are possible, but non-generic. Finally, we compare our findings with other models and laboratory experiments.
Keywords: granular gases, impact oscillators., inelastic collapse, Dynamical systems.
Mathematics Subject Classification: Primary: 37; Secondary: 76T25, 74M2.
Citation: Anna Maria Cherubini, Giorgio Metafune, Francesco Paparella. On the stopping time of a bouncing ball. Discrete and Continuous Dynamical Systems - B, 2008, 10 (1) : 43-72. doi: 10.3934/dcdsb.2008.10.43
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