eng
episciences.org
Communications in Mathematics
1804-1388
2336-1298
2021-04-30
Volume 29 (2021), Issue 1...
10.2478/cm-2021-0008
9527
journal article
The inverse problem in the calculus of variations: new developments
Thoan Do
Geoff Prince
https://orcid.org/0000-0003-4819-2219
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 Douglasâ€™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.
https://cm.episciences.org/9527/pdf
General Mathematics
[MATH]Mathematics [math]