Analysis of periodic-quasiperiodic nonlinear systems via Lyapunov-Floquet transformation and normal forms |
| |
Authors: | Susan M Wooden S C Sinha |
| |
Institution: | (1) Department of Mechanical Engineering, Nonlinear Systems Research Laboratory, Auburn University, Auburn, AL, 36849, U.S.A. |
| |
Abstract: | In this paper a general technique for the analysis of nonlinear dynamical systems with periodic-quasiperiodic coefficients
is developed. For such systems the coefficients of the linear terms are periodic with frequency ω while the coefficients of
the nonlinear terms contain frequencies that are incommensurate with ω. No restrictions are placed on the size of the periodic
terms appearing in the linear part of system equation. Application of Lyapunov-Floquet transformation produces a dynamically
equivalent system in which the linear part is time-invariant and the time varying coefficients of the nonlinear terms are
quasiperiodic. Then a series of quasiperiodic near-identity transformations are applied to reduce the system equation to a
normal form. In the process a quasiperiodic homological equation and the corresponding ‘solvability condition’ are obtained.
Various resonance conditions are discussed and examples are included to show practical significance of the method. Results
obtained from the quasiperiodic time-dependent normal form theory are compared with the numerical solutions. A close agreement is found. |
| |
Keywords: | Nonlinear systems Periodic Quasiperiodic Lyapunov-Floquet transformation Normal forms |
本文献已被 SpringerLink 等数据库收录! |