The inverse problem in the calculus of variations: new developments
Differential Geometry
2023-07-20 v1 Mathematical Physics
Dynamical Systems
math.MP
Optimization and Control
Abstract
We deal with the problem of determining the existence and uniqueness of Lagrangians for systems of 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 . We then examine a new class of solutions in arbitrary dimension and give some non-trivial examples in dimension 3
Cite
@article{arxiv.2001.06771,
title = {The inverse problem in the calculus of variations: new developments},
author = {Thoan Do and Geoff Prince},
journal= {arXiv preprint arXiv:2001.06771},
year = {2023}
}