Using a Moving Mass to Change the Spatial Orientation of a Rigid Body Subject to Time-Dependent External Forces

A mechanical system consisting of a rigid body and a material point is considered. They interact with each other by means of internal forces whose physical nature is not defined. Both objects are affected by external forces specified as functions of time. The task is to construct a trajectory for a point mass such that the solid body, under the action of the force of interaction with this mass, changes its orientation in space according to a predetermined program. Based on the theorem on the change in the relative moment of momentum, a second-order vector differential equation, unresolved with respect to the highest derivative, is obtained that describes the system. A change of variables is found that allows replacing the original equation with a first-order vector differential equation resolved with respect to the derivative. All special cases arising from the use of the new equation are considered. The obtained relationships can be used to control spacecraft and robotic systems.