An alternative form of the Helmholtz criterion in the inverse problem of the calculus of variations

Voronov, Theodore (2004) An alternative form of the Helmholtz criterion in the inverse problem of the calculus of variations. Letters in Mathematical Physics, 67 (2). pp. 103-110. ISSN 0377-9017

PDF An_Alternative_Form.pdf Restricted to Repository staff only Download (128kB)

Abstract

We give a necessary and sufficient condition for the existence of a local solution of the inverse problem of calculus of variations in terms of the identical vanishing of the variation of a functional on an extended space (with the number of independent variables increased by one), and explain its relation with the classical Helmholtz criterion using the de Rham complex on an infinite-dimensional space of fields.

Item Type:	Article
Uncontrolled Keywords:	calculus of variations - forms on field space - functionals - Helmholtz criterion
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 37 Dynamical systems and ergodic theory MSC 2010, the AMS's Mathematics Subject Classification > 49 Calculus of variations and optimal control; optimization MSC 2010, the AMS's Mathematics Subject Classification > 58 Global analysis, analysis on manifolds MSC 2010, the AMS's Mathematics Subject Classification > 70 Mechanics of particles and systems
Depositing User:	Ms Lucy van Russelt
Date Deposited:	16 Aug 2006
Last Modified:	20 Oct 2017 14:12
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/517

Actions (login required)

View Item