Forms of Lepage type and the balance systems

Abstract

In this work we apply infinitesimal variational calculus to the systems of balance equations. We determine a class of the exterior n + ( n + 1 ) -forms Θ on the jet bundle of infinite order over a configurational bundle π : Y n + m → X n similar to the class of Lepage n-forms. Systems of differential equations obtained in the way similar to one used in the Lagrangian field theory, include the Euler–Lagrange equations corresponding to a Lagrangian functions as well as arbitrary regular systems of balance equations. For a balance system with a symmetry group G we present the Noether balance laws corresponding to the generators of the Lie algebra of the group G.