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The inverse problem in the calculus of variations: new developments

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journal contribution
posted on 10.06.2021, 00:26 by Geoffrey PrinceGeoffrey Prince, Thi Kim Thoan DoThi Kim Thoan Do
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.

History

Publication Date

01/06/2021

Journal

Communications in Mathematics

Volume

29

Issue

1

Pagination

(p. 131-149)

Publisher

Sciendo

ISSN

2336-1298

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