EXISTENCE AND CONSTRUCTION OF DYNAMIC-SYSTEMS HAVING A PRESCRIBED INTEGRAL OF MOTION - AN INVERSE PROBLEM

Necessary and sufficient conditions for a given function Phi = Phi (x,y,x,y) are found so that the expression Phi =constant is an integral of motion of a planar dynamical system which is not given in advance. The cases of velocity-independent and velocity-dependent potentials are studied separately. In general, for each function Phi which satisfies certain conditions, the corresponding force field is determined uniquely. Certain degenerate cases, for which the force field is not determined uniquely are also studied. Several examples are offered.