On the stopping time of a bouncing ball

Anna Maria Cherubini; Giorgio Metafune; Francesco Paparella

doi:10.3934/dcdsb.2008.10.43

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2008, Volume 10, Issue 1: 43-72. Doi: 10.3934/dcdsb.2008.10.43

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On the stopping time of a bouncing ball

1.
Dipartimento di Matematica E. De Giorgi, Università del Salento, 73100, Lecce
2.
Dipartimento di Matematica e Fisica "Ennio De Giorgi", Università del Salento, 73100, Lecce

Received: May 31, 2007

Revised: December 31, 2007

Published: December 2007

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Abstract

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.

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Mathematics Subject Classification: Primary: 37; Secondary: 76T25, 74M20.

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