Construction of dynamically equivalent time-invariant forms for time-periodic systems
type: Item
instance of: scholarly article
title: Construction of dynamically equivalent time-invariant forms for time-periodic systems
zbMATH Open document ID: 0924.70021
DOI: 10.1023/A:1008072713385
published in: Nonlinear Dynamics
publication date: 1999-11-10T00:00:00Z
review text: The authors propose and develop several new general methods for constructing dynamically equivalent time-invariant forms for linear and nonlinear systems with periodic coefficients. The basis of these methods consists in the application of Lyapunov-Floquet transformation and simplification techniques such as center manifold reduction and time-dependent normal form theory. More specifically, in the first section it is shown that a set of linear second-order equations with periodic coefficients can be transformed to an equivalent set of time-invariant second-order equations by an application of a sequence of transformations. It is also shown that a time-periodic quadratic Hamiltonian can be transformed to a time-invariant Hamiltonian by extending this idea. In the second part the authors study time-invariant forms of nonlinear equations. Single and double inverted pendulums subjected to periodic parametric excitation are considered as physical examples of the presented techniques, and the obtained results are verified by numerical simulations.
Mathematics Subject Classification ID: 70K99
Mathematics Subject Classification ID: 70J99
Mathematics Subject Classification ID: 34C23
zbMATH DE Number: 1203544
zbMATH Keywords: critical systems
zbMATH Keywords: single pendulum
zbMATH Keywords: double inverted pendulum
zbMATH Keywords: nonlinear systems
zbMATH Keywords: periodic coefficients
zbMATH Keywords: Lyapunov-Floquet transformation
zbMATH Keywords: center manifold reduction
zbMATH Keywords: time-dependent normal form theory
zbMATH Keywords: time-periodic quadratic Hamiltonian
zbMATH Keywords: parametric excitation
author: S. C. Sinha
author: Eric A. Butcher
author: Alexandra Dávid
MaRDI profile type: Publication
full work available at URL: a:1008072713385
OpenAlex ID: W201412987
description: scientific article; zbMATH DE number 1203544