A maple® package for the calculus of variations based on jet manifolds

H Ennsbrunner and K Schlacher

Mathematical and Computer Modelling of Dynamical Systems, 2005, vol. 11, issue 1, 61-77

Abstract: 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 variables with respect to the independent ones. In the case of one independent variable, p = 1, the package derives the equations of motion in the form of a system of q ordinary differential equations of order 2 n , for p > 1 the result is a system of q partial differential equation up to the order 2 n . In addition the package determines all the required boundary conditions in the case of p ⩽ 3 and n ⩽ 2. Since the presented method uses the concept of jet manifolds, a short introduction to the notation of jet theory is provided. Two examples — the Timoshenko beam and the Kirchhoff plate — demonstrate the main features of the presented computer algebra based approach.

Date: 2005
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DOI: 10.1080/13873950500053056

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