Mathematical Problems in Engineering
Volume 2009 (2009), Article ID 409857, 13 pages
Can Drag Force Suppress Fermi Acceleration in a Bouncer Model?
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.
Some dynamical properties for a bouncer model—a classical particle of mass
falling in the
presence of a constant gravitational field
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.