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arXiv · 1110.5764

Symmetries of Helmholtz forms and globally variational dynamical forms

M. Palese·E. Winterroth
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Abstract

Invariance properties of classes in the variational sequence suggested to Krupka et al. the idea that there should exist a close correspondence between the notions of variationality of a differential form and invariance of its exterior derivative. It was shown by them that the invariance of a closed Helmholtz form of a dynamical form is equivalent with local variationality of the Lie derivative of the dynamical form, so that the latter is locally the Euler--Lagrange form of a Lagrangian. We show that the corresponding local system of Euler--Lagrange forms is variationally equivalent to a global Euler--Lagrange form.

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M. Palese, E. Winterroth. 2011-10-26. Symmetries of Helmholtz forms and globally variational dynamical forms. https://doi.org/10.1088/1742-6596/343/1/012129

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