On the stopping time of A bouncing ball

Anna Maria Cherubini, Giorgio Metafune, Francesco Paparella

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)43-72
Number of pages30
JournalDiscrete and Continuous Dynamical Systems - Series B
Issue number1
StatePublished - Jul 2008


  • Dynamical systems
  • Granular gases
  • Impact oscillators
  • Inelastic collapse

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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