Reconstruction of A Non-Stationary Potential of Gravitating System on Given Evolving Orbits

We study the problem of the reconstruction of a non-stationary space symmetrical regular planar potential of the gravitating system on a family of evolving types of orbits being used in the dynamics of stationary stellar systems. An application of such an inverse problem to the dynamical evolution of stellar systems with variable masses is given. The general form of the evolving orbit which we use when writing out the differential equations for non-stationary potential may also be interpreted as an osculating orbit of the perturbed Keplerian motion. In this case we are making an additional transformation of the basic equation of the problem and demonstrating an appropriate example of the construction of a non-stationary potential of a gravitating system. In connection with the stellar dynamical character of our inverse problem, we also give a generalized form of its basic equation in a rotating coordinate system.