Spatial Reorientation of a Solid Body Using a Moving Mass in the Presence of External Forces Specified as 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 moving along which a rigid body under the influence of the force of interaction with this mass that changes its orientation in space according to a known program. It is assumed that there are external forces acting on both objects, which are specified as functions of time. A system of three first-order ordinary differential equations, resolved with respect to derivatives, is obtained, which allows one to solve the problem. These relationships can be used to control spacecraft and robotic systems.