Skip to main content
Geometrical Model for a Particle on a Rough Inclined Surface
Mathematics and Statistics Faculty Publications and Presentations
  • Giovani L. Vasconcelos, Universidade Federal de Pernambuco
  • J. J. P. Veerman, Portland State University
Document Type
Publication Date
  • Dynamics,
  • Granular flow -- Mathematical models,
  • Chaotic behavior in systems

A simple geometrical model is presented for the gravity-driven motion of a single particle on a rough inclined surface. Adopting a simple restitution law for the collisions between the particle and the surface, we arrive at a model in which the dynamics is described by a one-dimensional map. This map is studied in detail and it is shown to exhibit several dynamical regimes (steady state, chaotic behavior, and accelerated motion) as the model parameters vary. A phase diagram showing the corresponding domain of existence for these regimes is presented. The model is also found to be in good qualitative agreement with recent experiments on a ball moving on a rough inclined line.


This is the author’s version of a work that was accepted for publication in Physical Review E. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication.

A definitive version was subsequently published in Physical Review E and can be found online at:

* At the time of publication J. J. P. Veerman was affiliated with Universidade Federal de Pernambuco

Persistent Identifier
Citation Information
Giovani L. Vasconcelos and J. J. P. Veerman. "Geometrical Model for a Particle on a Rough Inclined Surface" (1999)
Available at: