De Donder Construction for Higher Jets

Abstract

In this paper, we generalize De Donder approach to construct boundary forms that depend on the adapted coordinate system used. In continuum mechanics, use of boundary forms leads to splitting of the total force acting on the body into body force and surface traction. Moreover, this splitting is independent of the choice of the boundary form used. In calculus of variations, use of boundary forms leads to equations in exterior differential forms that are equivalent to the Euler-Lagrange equations. Infinitesimal symmetries of the theory lead to conservation laws valid for any choice of the boundary form used. In an example, we show that the boundary conditions lead to independence of constants of motion of the choice of the boundary form.