The inverse problem in the calculus of variations: new developments

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

Cited by in corpus (3)

• Almost every path structure is not variational
• Variationality of conformal geodesics in dimension 3
• Linear connections and shape maps for second order ODEs with and without constraints