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.
Vasconcelos, Giovani L. and Veerman, J. J. P., "Geometrical Model for a Particle on a Rough Inclined Surface" (1999). Mathematics and Statistics Faculty Publications and Presentations. 149.