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Mathematical Problems in Engineering
Volume 2009 (2009), Article ID 298906, 40 pages
Research Article

Motion Switching and Chaos of a Particle in a Generalized Fermi-Acceleration Oscillator

Department of Mechanical and Industrial Engineering, Southern Illinois University Edwardsville, Edwardsville, IL 62026-1805, USA

Received 23 September 2008; Revised 21 December 2008; Accepted 26 January 2009

Academic Editor: Edson Denis Leonel

Copyright © 2009 A. C. J. Luo and Y. Guo. 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.


Dynamic behaviors of a particle (or a bouncing ball) in a generalized Fermi-acceleration oscillator are investigated. The motion switching of a particle in the Fermi-oscillator causes the complexity and unpredictability of motion. Thus, the mechanism of motion switching of a particle in such a generalized Fermi-oscillator is studied through the theory of discontinuous dynamical systems, and the corresponding analytical conditions for the motion switching are developed. From solutions of linear systems in subdomains, four generic mappings are introduced, and mapping structures for periodic motions can be constructed. Thus, periodic motions in the Fermi-acceleration oscillator are predicted analytically, and the corresponding local stability and bifurcations are also discussed. From the analytical prediction, parameter maps of periodic and chaotic motions are achieved for a global view of motion behaviors in the Fermi-acceleration oscillator. Numerical simulations are carried out for illustrations of periodic and chaotic motions in such an oscillator. In existing results, motion switching in the Fermi-acceleration oscillator is not considered. The motion switching for many motion states of the Fermi-acceleration oscillator is presented for the first time. This methodology will provide a useful way to determine dynamical behaviors in the Fermi-acceleration oscillator.