Can Drag Force Suppress Fermi Acceleration in a Bouncer Model?

Abstract

Some dynamical properties for a bouncer model-a classical particle of mass m falling in the presence of a constant gravitational field g and hitting elastically a periodically moving wall-in the presence of drag force that is assumed to be proportional to the particle's velocity are studied. The dynamics of the model is described in terms of a two-dimensional nonlinear mapping obtained via solution of the second Newton's law of motion. We characterize the behavior of the average velocity of the particle as function of the control parameters as well as the time. Our results show that the average velocity starts growing at first and then bends towards a regime of constant value, thus confirming that the introduction of drag force is a sufficient condition to suppress Fermi acceleration in the model. Copyright (C) 2009 Francys Andrews de Souza et al.