The energetic/variational interpretation of Poincaré's criterion for the orbital stability of limit cycles of autonomous systems
type: Item
instance of: scholarly article
title: The energetic/variational interpretation of Poincaré's criterion for the orbital stability of limit cycles of autonomous systems
zbMATH Open document ID: 0618.70011
DOI: 10.1016/0020-7225(87)90122-4
author: John G. Papastavridis
published in: International Journal of Engineering Science
publication date: 1987-01-01T00:00:00Z
review text: A proof of the Poincaré criterion for orbital stability of limit cycles of autonomous systems is given by \textit{J. J. Stoker} [Nonlinear vibrations in mechanical and electrical systems (1950; Zbl 0035.396)] based on phase-space methods. A version of the proof has also been presented by \textit{S. W. McCuskey} [An introduction to advanced dynamics (1959; Zbl 0082.171)]. According to the author the only other existing proof is based on the theory of characteristic exponents [see \textit{R. E. Mickens}, An introduction to nonlinear oscillations (1981; Zbl 0459.34002)]. The author summarizes the Stoker/McCuskey proof, and then developes a new proof based on Lagrangian/Hamiltonian variational principles.
Mathematics Subject Classification ID: 70K05
Mathematics Subject Classification ID: 37G15
Mathematics Subject Classification ID: 70H03
Mathematics Subject Classification ID: 37J99
Mathematics Subject Classification ID: 70G10
zbMATH DE Number: 4003576
zbMATH Keywords: Poincaré criterion
zbMATH Keywords: orbital stability
zbMATH Keywords: limit cycles
zbMATH Keywords: autonomous systems
zbMATH Keywords: phase-space methods
zbMATH Keywords: characteristic exponents
zbMATH Keywords: nonlinear oscillations
zbMATH Keywords: Hamiltonian variational principles
MaRDI profile type: Publication
full work available at URL: 0020-7225(87)90122-4
OpenAlex ID: W2083955871
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description: scientific article; zbMATH DE number 4003576