Abstract
In the new formulation, the translational-rotational motion of a non-stationary axisymmetric body under the gravitational influence of two spherical bodies with time-varying masses is considered. The non-stationarity of the axisymmetric body is characterized by changes in its mass, dimensions, and compression along its axis of symmetry. Additionally, the axisymmetric body is assumed to possess an equatorial plane of symmetry. This case is examined within a specialized version of the non-stationary restricted three-body problem. The problem becomes significantly more complex due to the time-dependent changes in the masses and dimensions of the bodies, which may also generate reactive forces. Equations of motion for the problem under consideration have been derived in both absolute and relative coordinate systems. For the first time, the equations of motion for the barycenter of two spherical bodies with variable masses, accounting for reactive forces, have been obtained. Based on these equations, the equations of motion for the problem in the barycentric coordinate system have also been derived. Keywords: restricted three-body problem, variable mass, non – stationary axisymmetric celestial bodies, translational-rotational motion.