An EDS approach to the inverse problem in the calculus of variations

The inverse problem in the calculus of variations for a given set of second-order ordinary differential equations consists of deciding whether their solutions are those of Euler-Lagrange equations and whether the Lagrangian, if it exists, is unique. This paper discusses the exterior differential systems approach to this problem. In particular, it proposes an algorithmic procedure towards the construction of a certain differential ideal. The emphasis is not so much on obtaining a complete set of integrability conditions for the problem, but rather on producing a minimal set to expedite the differential ideal process. (c) 2006 American Institute of Physics.