The Helmholtz conditions in terms of constants of motion in classical mechanics
- 1 September 1989
- journal article
- conference paper
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 30 (9) , 2054-2061
- https://doi.org/10.1063/1.528243
Abstract
The Helmholtz conditions are the necessary and sufficient conditions for a set of second-order differential equations to be equivalent to a variational principle. In this work an alternative approach to the inverse problem in classical mechanics is described. It is proven that the Helmholtz conditions can be transformed into a set of conditions for a nonsingular antisymmetric matrix whose entries are constants of motion of the problem in question.Keywords
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