A study of conservation laws of dynamical systems by means of the differential variational principles of Jourdain and Gauss
type: Item
instance of: scholarly article
title: A study of conservation laws of dynamical systems by means of the differential variational principles of Jourdain and Gauss
zbMATH Open document ID: 0612.70017
DOI: 10.1007/BF01176873
published in: Acta Mechanica
publication date: 1987-01-01T00:00:00Z
review text: The author shows that the differential variational principles of Jourdain and Gauss can be employed as a starting point for the study of conservation laws of conservative and nonconservative systems with a finite number of degrees of freedom. He demonstrates that the introduction of the generalized (nonsimultaneous) variations in the sense of Jourdain and Gauss yields a Noether's-type theory for finding conservation laws. For the case of conservative systems, the outcome is identical with the classical Noether-theory. As a characteristic feature of the theory, the condition of the invariance of the Gauss constraint with respect to the infinitesimal transformations of the acceleration vector (including the time deformation) produces the condition for the existence of a conserved quantity (the basic Noether identity and corresponding conservation laws. Generally, it is difficult to select appropriate functions appearing in a basic identity.
Mathematics Subject Classification ID: 70H30
Mathematics Subject Classification ID: 49S05
zbMATH DE Number: 3990934
zbMATH Keywords: differential variational principles of Jourdain
zbMATH Keywords: conservation laws
zbMATH Keywords: nonconservative systems
zbMATH Keywords: finite number of degrees of freedom
zbMATH Keywords: classical Noether-theory
zbMATH Keywords: Gauss constraint
zbMATH Keywords: infinitesimal transformations
zbMATH Keywords: Noether identity
author: B. D. Vujanović
MaRDI profile type: Publication
cites work: Noether's theory in classical nonconservative mechanics
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full work available at URL: https://doi.org/10.1007/bf01176873
OpenAlex ID: W2017140944
description: scientific article; zbMATH DE number 3990934