Symmetries and constants of the motion for singular Lagrangian systems
type: Item
instance of: scholarly article
title: Symmetries and constants of the motion for singular Lagrangian systems
zbMATH Open document ID: 0856.58034
DOI: 10.1007/BF02302383
author: Manuel de León
author: David Martín de Diego
published in: International Journal of Theoretical Physics
publication date: 1996-08-25T00:00:00Z
review text: The merit of this paper is that it presents a coherent survey of the story of symmetries and conservation laws for a number of fairly related yet different situations of degeneracy in the dynamical system. The authors first discuss the classification of symmetries and a Noether-type theorem for presymplectic systems, with special attention for the case of existence of a global dynamics. The results are applied to singular Lagrangian systems and shown to be in good correspondence with the Hamiltonian picture for such systems. Separate short sections are devoted to: the problem of obtaining a reduced second-order system which is equivalent via the Legendre map to the Hamiltonian system on the final constraint submanifold; the rather exotic construction for regular Lagrangian systems of a presymplectic system on the Whitney sum of the tangent and cotangent bundle; the case of a Lagrangian which is linear in the velocities; the reduction of degenerate Lagrangian systems of type II; degenerate systems which admit a presymplectic action of a Lie group. The final section is about precosymplectic systems as a model for the study of symmetries and conservation laws of time-dependent degenerate Lagrangians.
Mathematics Subject Classification ID: 37J15
Mathematics Subject Classification ID: 70H03
Mathematics Subject Classification ID: 70G45
Mathematics Subject Classification ID: 70H33
zbMATH DE Number: 896378
zbMATH Keywords: presymplectic systems
zbMATH Keywords: conservation laws
zbMATH Keywords: symmetries
zbMATH Keywords: degenerate Lagrangians
reviewed by: W. Sarlet
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02302383
OpenAlex ID: W2081181544
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description: scientific article; zbMATH DE number 896378