The inverse problem for flat kinetic minus potential Lagrangians (Q2766071)

The purpose of this paper is to solve a restricted version of the inverse problem. The inverse problem of the calculus of variations asks for necessary and sufficient conditions that a given system of second-order ordinary differential equations should be Euler-Lagrange equations of a regular Lagrangian function. Here the authors give sufficient conditions which imply the existence of solutionfor a unique Lagrangian of classical mechanical type, that is, of the form flat-metric kinetic energy minus potential. The result may be said to describe all ordinary differential equations that are of generic classical mechanical type.