Spatial reorientation of a solid body using a moving mass in the presence of external forces specified as the functions of time

The spatial motion of a mechanical system consisting of a rigid body and a moving point mass, interacting with each other by means of unspecified internal forces, has been studied. The task is to construct such a trajectory for a point mass, when moving along which a rigid body, under the influence of the force of interaction with this mass, changes its orientation in space according to a known program. It is assumed that there are external forces acting on both objects, specified as functions of time. A system of three first-order ordinary differential equations, resolved with respect to derivatives, is obtained, which allows solving the problem. These relationships can be used to control spacecraft and robotic systems.