THE INVERSE JACOBI PROBLEM

The paper presents a discussion of the relation between the dynamics o f a mechanical system based upon a Lagrangian admitting energy conserv ation and the dynamics based upon its Jacobi Lagrangian, which determi nes the space trajectories of the system. The basic result found in th e paper is the general solution of the inverse problem, i.e. how to de termine the full Lagrangian, when as a starting point, an arbitrary ho mogeneous Lagrangian, which is used to determine the space trajectorie s of a system, and an arbitrarily assigned energy function which speci fies the interaction of the system are given.