Poincaré-Cartan integral invariants of nonconservative dynamical systems
type: Item
instance of: scholarly article
title: Poincaré-Cartan integral invariants of nonconservative dynamical systems
zbMATH Open document ID: 0966.37004
DOI: 10.1023/A:1026689926165
published in: International Journal of Theoretical Physics
publication date: 1999-11-18T00:00:00Z
review text: In this paper the authors review some results on the Poincaré and Poincaré-Cartan integral invariants from the traditional point of view and discuss the adjoint symmetries of a system of \(n\) second-order ordinary differential equations. For weak nonconservative systems the authors prove that a system of dynamical equations and their adjoint equations are canonical in an extended phase space and there exist integral invariants in the space. Integral invariants for pseudoconservative systems are constructed. The one-dimensional damped vibration is reanalyzed. It is shown that the Poincaré and Poincaré-Cartan integral invariants exist in the extended phase space.
Mathematics Subject Classification ID: 37C15
Mathematics Subject Classification ID: 34C14
zbMATH DE Number: 1364342
zbMATH Keywords: pseudoconservative system
zbMATH Keywords: Poincaré-Cartan invariant
author: YongXin Guo
author: M. Shang
author: Fengxiang Mei
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1364342