A geometrical version of the Helmholtz conditions in time-dependent Lagrangian dynamics
- 11 May 1984
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 17 (7) , 1437-1447
- https://doi.org/10.1088/0305-4470/17/7/011
Abstract
Appropriate geometrical machinery for the study of time-dependent Lagrangian dynamics is developed. It is applied to the inverse problem of the calculus of variations, and a set of necessary and sufficient conditions for the existence of a Lagrangian are given, in terms of the existence of a 2-form with suitable properties, which are exactly equivalent to the Helmholtz conditions.Keywords
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