Geometric aspects of nonholonomic field theories

Abstract

A geometric model for nonholonomic Lagrangian field theory is studied. The multisymplectic approach to such a theory as well as the corresponding Cauchy formalism are discussed. It is shown that in both formulations, the relevant equations for the constrained system can be recovered by a suitable projection of the equations for the underlying free (i.e. unconstrained) Lagrangian system.

arXiv comment29 pages; typos removed

References in corpus (7)

• Variational methods, multisymplectic geometry and continuum mechanics
• Momentum Maps and Classical Relativistic Fields. Part I: Covariant Field Theory
• Momentum Maps and Classical Relativistic Fields. Part II: Canonical Analysis of Field Theories
• Symmetries in Classical Field Theory
• Geometric Structures in Field Theory
• Tulczyjew's triples and lagrangian submanifolds in classical field theories
• Nonholonomic constraints in classical field theories

Cited by in corpus (13)

• Multisymplectic Lagrangian and Hamiltonian Formalisms of Classical Field Theories
• Extended Hamiltonian systems in multisymplectic field theories
• The Hamilton-Pontryagin Principle and Multi-Dirac Structures for Classical Field Theories
• The Tulczyjew triple for classical fields
• A class of nonholonomic kinematic constraints in elasticity
• The Herglotz variational principle for dissipative field theories
• Multi-Dirac Structures and Hamilton-Pontryagin Principles for Lagrange-Dirac Field Theories
• Symmetry aspects of nonholonomic field theories
• Hamilton-Jacobi theory for gauge field theories
• Chetaev vs. vakonomic prescriptions in constrained field theories with parametrized variational calculus
• A general framework for nonholonomic mechanics: Nonholonomic Systems on Lie affgebroids
• Nonholonomic constraints in $k$-symplectic Classical Field Theories
• The rotating rigid body model based on a non-twisting frame