Secular perturbations of the translational-rotational motion in a nonstationary three-body problem

Abstract

A non-stationary three-body problem with axisymmetric dynamic structure, shape, and variable compression is considered. The Newtonian interaction force is characterized by an approximate expression of the force function accurate to the second harmonic. The masses of bodies change isotropically at different rates. The axes of inertia of the proper coordinate system of nonstationary axisymmetric three bodies coincide with the principal axes of inertia of the bodies, and it is assumed that their relative orientations remain unchanged during the evolution. Differential equations of translational and rotational motion of three non-stationary axisymmetric bodies with variable masses and dimensions in the relative coordinate system with the origin in the center of the more massive body are presented. The analytical expression for the Newtonian force function of the interaction of three bodies with variable masses and dimensions is given. The canonical equations of translational-rotational motion of three bodies in the Delaunaye-Andouye analogues have been obtained. The equations of secular perturbations of translational-rotational motion of unsteady axisymmetric three-bodies in the analogue of the Delaunaye-Andouye osculating elements have been obtained. The problem is investigated by methods of perturbation theory.