Motion switching and chaos of a particle in a generalized Fermi-acceleration oscillator
type: Item
instance of: scholarly article
title: Motion switching and chaos of a particle in a generalized Fermi-acceleration oscillator
zbMATH Open document ID: 1331.70062
DOI: 10.1155/2009/298906
author: Albert C. J. Luo
author: Yu Guo
published in: Mathematical Problems in Engineering
publication date: 2009-11-13T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 70K55
Mathematics Subject Classification ID: 82C03
zbMATH DE Number: 5632465
Wikidata QID: Q58648944
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2009/298906
OpenAlex ID: W2064469220
cites work: On the Origin of the Cosmic Radiation
cites work: Q3293254
cites work: Regular and chaotic dynamics.
cites work: Poincaré models, rigorous justification of the second element of thermodynamics on the basis of mechanics, and the Fermi acceleration mechanism
cites work: A bouncing ball model with two nonlinearities: a prototype for Fermi acceleration
cites work: The presence and lack of Fermi acceleration in nonintegrable billiards
cites work: Scaling features of a breathing circular billiard
cites work: The dynamics of repeated impacts with a sinusoidally vibrating table
cites work: Stable periodic motions of an impact-pair
cites work: A periodically forced piecewise linear oscillator
cites work: Global dynamics of a vibro-impacting linear oscillator
cites work: Dynamical complexities of forced impacting systems
cites work: Chattering and related behaviour in impact oscillators
cites work: Analytical determination of bifurcations in an impact oscillator
cites work: The general motion of an inclined impact damper with friction
cites work: Period-doubling induced chaotic motion in the LR model of a horizontal impact oscillator
cites work: The mapping dynamics of periodic motions for a three-piecewise linear system under a periodic excitation
cites work: Local Langlands duality and a duality of conformal field theories
cites work: Q3596254
cites work: Stick and non-stick periodic motions in periodically forced oscillators with dry friction
cites work: On flow switching bifurcations in discontinuous dynamical systems
cites work: Q5386147
cites work: A theory for flow switchability in discontinuous dynamical systems
description: scientific article; zbMATH DE number 5632465