The inverse problem in the calculus of variations: new developments
journal contributionposted on 2021-06-10, 00:26 authored 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.