Reduction of degenerate Lagrangian systems
type: Item
instance of: scholarly article
title: Reduction of degenerate Lagrangian systems
zbMATH Open document ID: 0621.58020
DOI: 10.1016/0393-0440(86)90014-8
published in: Journal of Geometry and Physics
publication date: 1986-01-01T00:00:00Z
review text: Let a degenerate Lagrangian L be given on some velocity phase space (i.e. a tangent bundle). Is it possible to construct another velocity space and a regular Lagrangian which contains the same dynamical information as L ? This important question is referred to as the ''regularization problem'' for degenerate Lagrangians. The authors find conditions which guarantee the existence of such a regularization and describe a relevant class of Lagrangians for which the above question admits an affirmative answer. The connection with the canonical approach to the regularization problem of degenerate systems (Dirac's theory) and the reduction of systems with symmetry (Marsden-Weinstein theory) is also discussed. The paper is completed with a few typical examples and applications. Two appendices are devoted to the proof of those intermediate results which are of interest on their own.
Mathematics Subject Classification ID: 37J99
Mathematics Subject Classification ID: 53C15
Mathematics Subject Classification ID: 70H03
Mathematics Subject Classification ID: 53C80
zbMATH DE Number: 4007291
zbMATH Keywords: tangent bundle geometry
zbMATH Keywords: degenerate Lagrangian
zbMATH Keywords: regularization problem
zbMATH Keywords: reduction
author: F. Cantrijn
author: J. F. Cariñena
author: Mike Crampin
author: Luis A. Ibort
reviewed by: József Szilasi
MaRDI profile type: Publication
full work available at URL: 0393-0440(86)90014-8
OpenAlex ID: W1974243870
cites work: On the Analogy Between Classical and Quantum Mechanics
cites work: Presymplectic manifolds and the Dirac–Bergmann theory of constraints
cites work: Reduction of symplectic manifolds with symmetry
cites work: Q5588452
cites work: Q3049554
cites work: Q3900713
cites work: Espaces variationnels et mécanique
cites work: Tangent bundle geometry Lagrangian dynamics
cites work: Structure presque tangente et connexions. I
cites work: Geometric theory of the equivalence of Lagrangians for constrained systems
cites work: On the differential geometry of the Euler-Lagrange equations, and the inverse problem of Lagrangian dynamics
cites work: A new look at second-order equations and Lagrangian mechanics
cites work: Affine bundles and integrable almost tangent structures
cites work: Integrable almost tangent structures
cites work: Q3696183
cites work: Q3469562
cites work: Q4192639
cites work: Q4174811
cites work: Dirac Bracket Transformations in Phase Space
cites work: Constrained dynamics. With applications to Yang-Mills theory, general relativity, classical spin, dual string model
cites work: Q4148478
cites work: Q5545212
cites work: Q5736745
cites work: Q5633692
cites work: On the three-dimensional lunar problem and other perturbation problems of the Kepler problem
cites work: Generalized canonical transformations for time-dependent systems
cites work: Canonical variables for the Dirac theory
description: scientific article; zbMATH DE number 4007291