A Maple Package for Calculus of Variations based on Field Theory

This contribution presents a computer algebra package for Lagrangian systems with p>=1 independent and q>=1 dependent variables. The Lagrangian may depend on the partial derivatives up to the order n>=0 of the dependent varibales with respect to the independent ones. In the case of one independent variable, p=1, the packages derives the equations of motion in form of a system of q ordinary differenital equations of order 2n, for p>1 the result is a system of q partial differential equation up to the order 2n.In addition the package determines all the required boundary conditions. Since the presented methods uses the concept of jet manifolds, a short introductuion to the notation of jet theory is provided. A simple example, the Timoshenko beam, demonstrates the main features of the presented computer algebra based appraoch.