Differential equations with constraints in jet bundles: Lagrangian and Hamiltonian systems
type: Item
instance of: scholarly article
title: Differential equations with constraints in jet bundles: Lagrangian and Hamiltonian systems
zbMATH Open document ID: 1116.58002
author: Olga Rossi
author: Petr Volný
published in: Lobachevskii Journal of Mathematics
publication date: 2007-04-11T00:00:00Z
full work available at URL: https://eudml.org/doc/231774
full work available at URL: 113.html
review text: The authors present a survey of the theory of Lagrangian systems with non-holonomic constraints in jet bundles. The exposition deals with systems of second-order ordinary and partial differential equations that arise as extremals of variational functionals in fibered manifolds. A geometrical setting for Euler-Lagrange and Hamilton equations, based on the concept of Lepage class is presented. A constraint is modeled in the underlying fibered manifold as a fibered submanifold endowed with a distribution (the canonical distribution). A constrained system is defined by means of a Lepage class on the constraint submanifold. Constrained Euler-Lagrange equations and constrained Hamilton equations and properties of the corresponding exterior differential systems, such as regularity, canonical form, or existence of a constraint Legendre transformation, are presented. The cases of mechanics (ODEs) and field theory (PDEs) are investigated separately; still, the exposition is unitary, which permits a direct comparison of results and formulas. It should be noted that, although the paper is of review type, it contains new results regarding constrained Hamilton-De Donder equations and constraint Legendre transformation for general non-holonomic constraints in field theory.
reviewed by: Vladimir Balan
Mathematics Subject Classification ID: 58A20
Mathematics Subject Classification ID: 35A30
Mathematics Subject Classification ID: 70H03
Mathematics Subject Classification ID: 70H05
zbMATH DE Number: 5141815
zbMATH Keywords: jet bundles
zbMATH Keywords: differential equations
zbMATH Keywords: non-holonomic constraints
zbMATH Keywords: Lagrangian systems
zbMATH Keywords: Hamiltonian systems
zbMATH Keywords: Lepage classes
zbMATH Keywords: dynamical forms
zbMATH Keywords: locally variational forms
zbMATH Keywords: Hamilton-De Donder equations
zbMATH Keywords: Euler-Lagrange equations
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5141815