Abstract. The paper presents a discussion of the relation between the dynamics of a mechanical system based upon a Lagrangian admitting energy conservation and the dynamics based upon its Jacobi Lagrangian, which determines the space trajectories of the system. The basic result found in the paper is the general solution of the inverse problem, i.e. how to determine the full Lagrangian, when as a starting point, an arbitrary homogeneous Lagrangian, which is used to determine the space trajectories of a system, and an arbitrarily assigned energy function which specifies the interaction of the system are given.

Print publication: Issue 9 (7 May 1994)