How to recover a Lagrangian using the homogeneous variational bicomplex
Differential Geometry
2007-05-23 v1
Abstract
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.
Cite
@article{arxiv.math/0612587,
title = {How to recover a Lagrangian using the homogeneous variational bicomplex},
author = {D. J. Saunders},
journal= {arXiv preprint arXiv:math/0612587},
year = {2007}
}