MODELING OF VARIATIONAL DYNAMICAL SYSTEMS: THE INVERSE PROBLEM OF THE CALCULUS OF VARIATIONS

In this paper we discuss a classification of systems of two second-order ordinary differential equations with respect to the inverse problem of the calculus of variations. Foundations for this classification were given by Jesse Douglas in 1941, and in the next years it was worked tip by many other authors. The solution of the problem means to analyse conditions to be satisfied for a system of functions be variational. We propose a new look at the classification which simplifies the procedure of solving concrete examples.