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- Title
A GLOBAL PERIOD-1 MOTION OF A PERIODICALLY EXCITED, PIECEWISE-LINEAR SYSTEM.
- Authors
Menon, Santhosh; Luo, Albert C. J.
- Abstract
The period-1 motion of a piecewise-linear system under a periodic excitation is predicted analytically through the Poincaré mapping and the corresponding mapping sections formed by the switch planes pertaining to the two constraints. The mapping relationship generates a set of nonlinear algebraic equations from which the period-1 motion is determined analytically. The stability and bifurcation of the period-1 motion are determined, and numerical simulations are carried out for confirmation of the analytical prediction of period-1 motion. An unsymmetrical stable period-1 motion is observed. This investigation helps us understand the dynamical behavior of period-1 motion in the piecewise-linear system and more efficiently obtain other periodic motions and chaos through numerical simulations. The similar methodology presented in this paper can be used for other nonsmooth dynamical systems.
- Subjects
LINEAR systems; SYSTEMS theory; POINCARE series; NONSMOOTH optimization; MATHEMATICAL optimization; MATHEMATICAL analysis; MATHEMATICS
- Publication
International Journal of Bifurcation & Chaos in Applied Sciences & Engineering, 2005, Vol 15, Issue 6, p1945
- ISSN
0218-1274
- Publication type
Article
- DOI
10.1142/S0218127405013071