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arXiv · 2001.06771

The inverse problem in the calculus of variations: new developments

Thoan Do·Geoff Prince
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Abstract

We deal with the problem of determining the existence and uniqueness of Lagrangians for systems of $n$ second order ordinary differential equations. A number of recent theorems are presented, using exterior differential systems theory (EDS). In particular, we indicate how to generalise Jesse Douglas's famous solution for $n=2$. We then examine a new class of solutions in arbitrary dimension $n$ and give some non-trivial examples in dimension 3

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BibTeXRIS

Thoan Do, Geoff Prince. 2020-01-19. The inverse problem in the calculus of variations: new developments. https://doi.org/10.2478/cm-2021-0008

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