Geometric aspects of nonholonomic field theories

TL;DR

This paper explores the geometric structure of nonholonomic field theories, demonstrating how constrained equations can be derived from unconstrained systems using a multisymplectic approach and Cauchy formalism.

Contribution

It introduces a geometric model for nonholonomic Lagrangian field theories and shows how to obtain constrained equations via projection from free systems.

Findings

Constrained equations are recoverable by projection from unconstrained systems.

The multisymplectic approach effectively describes nonholonomic field theories.

The Cauchy formalism provides a consistent framework for these 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.