Mathematical Problems in Engineering
Volume 2009 (2009), Article ID 409857, 13 pages
doi:10.1155/2009/409857
Research Article

Can Drag Force Suppress Fermi Acceleration in a Bouncer Model?

Francys Andrews de Souza,1 Lucas Eduardo Azevedo Simões,1 Mário Roberto da Silva,2 and Edson D. Leonel2

1Departamento de Matemática, Instituto de Geociências e Ciências Exatas, Universidade Estadual Paulista, Avenida 24A, 1515, Bela Vista, 13506-900 Rio Claro, SP, Brazil
2Departamento de Estatística, Matemática Aplicada e Computação, Universidade Estadual Paulista, Avenida 24A, 1515, Bela Vista, 13506-900 Rio Claro, SP, Brazil

Received 14 April 2009; Accepted 20 July 2009

Academic Editor: Alexander Loskutov

Copyright © 2009 Francys Andrews de Souza et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.