Thoan Do, Geoff Prince
Published 2020-01-19Version 1
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
New progress in the inverse problem in the calculus of variations
The inverse problem of the calculus of variations for discrete systems
Isotropic submanifolds and the inverse problem for mechanical constrained systems
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