Geometrical model for a particle on a rough inclined surface

Details Geometrical model for a particle on a rough inclined surface Geometrical model for a particle on a rough inclined surface

1999-04-09

arxiv.org/abs/cond-mat/9904139v1

Physics

Condensed Matter

Soft Condensed Matter

6pages, 6 figures, to appear in Phys. Rev. E (May 1999)

Scientific paper

10.1103/PhysRevE.59.5641

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.

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