Dynamics of a single particle in a horizontally shaken box

Details Dynamics of a single particle in a horizontally shaken box Dynamics of a single particle in a horizontally shaken box

1997-09-18

arxiv.org/abs/chao-dyn/9709021v1

Physics

Condensed Matter

11 pages RevTex. Some postscript files have low resolution. We will send the high-resolution files on request

Scientific paper

10.1007/s100510050216

We study the dynamics of a particle in a horizontally and periodically shaken box as a function of the box parameters and the coefficient of restitution. For certain parameter values, the particle becomes regularly chattered at one of the walls, thereby loosing all its kinetic energy relative to that wall. The number of container oscillations between two chattering events depends in a fractal manner on the parameters of the system. In contrast to a vertically vibrated particle, for which chattering is claimed to be the generic fate, the horizontally shaken particle can become trapped on a periodic orbit and follow the period-doubling route to chaos when the coefficient of restitution is changed. We also discuss the case of a completely elastic particle, and the influence of friction between the particle and the bottom of the container.

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