Euler-Lagrange and Hamilton equations for non-holonomic systems in field theory

Abstract

A generalization of the concept of a system of non-holonomic constraints to fibred manifolds with n-dimensional bases is considered. Motion equations in both Lagrangian and Hamiltonian settings for systems subjected to such constraints are investigated. Regularity conditions for the existence of a non-holonomic Legendre transformation, and the corresponding formulae for Hamiltonian and momenta are found. In particular, Lagrangian constraints and semi-holonomic constraints, and simplifications arising in this case are discussed.