The inverse problem in the calculus of variations: new developments-Reference-Cited by-同舟云学术

The inverse problem in the calculus of variations: new developments

Published:2021-04-30 Issue:1 Volume:29 Page:131-149
ISSN:2336-1298
Container-title:Communications in Mathematics
language:en
Short-container-title:

Author:

Do Thoan¹,Prince Geoff²

Affiliation:

1. Department of Mathematics and Statistics , La Trobe University , Victoria 3086 , Australia and Department of Mathematics , Can Tho University , Vietnam

2. Department of Mathematics and Statistics , La Trobe University , Victoria 3086 , Australia

Abstract

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.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Reference23 articles.

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4. [4] R.L. Bryant, S.S. Chern, R.B. Gardner, H.L. Goldschmidt, P.A. Gri ths: Exterior Differential Systems. Springer (1991).

5. [5] M. Crampin, E. Martínez, W. Sarlet: Linear connections for systems of second–order ordinary differential equations. Ann. Inst. H. Poincaré Phys. Théor. 65 (1996) 223–249.

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