THE INVERSE PROBLEM OF DYNAMICS FOR SYSTEMS WITH NONSTATIONARY LAGRANGIAN

We construct a non-stationary form of the Lagrangian of a material poi nt with a known integral of motion and given monoparametric family of evolving orbits. An equation for nonstationary space symmetrical 'pote ntial' function of such Lagrangian is given and this stands for the an alog of Szebehely's (1974) equation. As an application of the problem, an integrable equation from celestial mechanics of variable mass with use of non-perturbed orbits of evolving type is constructed. On its b asis adiabatic invariants of non-stationary two-body problem containin g a tangential force are found.