Chaotic or just complicated? Ball bouncing down the stairs

Márton Gruiz, Tamás Meszéna, Tamás Tél

Research output: Contribution to journalArticle

1 Citation (Scopus)


The aim of this study is to investigate the bouncing dynamics of a small elastic ball on a rectangular stairway and to determine if its dynamics is chaotic. We derive a simple nonlinear recursion for the coordinates of the collisions from which the type of dynamics cannot be predicted. Numerical simulations indicate that stationary bouncing always sets in asymptotically, and is typically quasi-periodic. The dependence on the coefficient of restitution can be very complicated, yet the dynamics is found to be nonchaotic. Only elementary mathematics is required for the calculations, and we offer a piece of user-friendly demo software on our website,, to facilitate further understanding of this complex phenomenon.

Original languageEnglish
Article number055003
JournalEuropean Journal of Physics
Issue number5
Publication statusPublished - Aug 16 2017


  • attractors
  • billiard
  • bouncing dynamics
  • coefficient of restitution
  • gravity
  • quasi-periodic motion
  • stair

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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