How to recover a Lagrangian using the homogeneous variational bicomplex

Details How to recover a Lagrangian using the homogeneous variational bicomplex How to recover a Lagrangian using the homogeneous variational bicomplex

2006-12-20

arxiv.org/abs/math/0612587v1

Mathematics

Differential Geometry

Scientific paper

We show how the homogeneous variational bicomplex provides a useful formalism for describing a number of properties of single-integral variational problems, and we introduce a subsequence of one of the rows of the bicomplex which is locally exact with respect to the variational derivative. We are therefore able to recover a Lagrangian from a set of equations given as a variationally-closed differential form. As an example, we show how to recover a first-order Lagrangian from a suitable set of second-order equations.

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