Control of the motion of a solid rotating about its centre of mass

Abstract Problems of controlling the spherical motion of a rotating solid when the controlling torques delivered to the body by the controls do not contain an x -component and their axes are not the principal central axes of inertia of the body are investigated. It is shown that as the transverse components of the angular velocity vector are suppressed and the orientation of the non-principal axis of inertia of the body stabilizes, there is an accompanying drop in the angular velocity of twist and, in the final analysis, the rotating body loses its gyroscopic properties. On the other hand, control of the uniform rotation of the body about a principal axis of inertia and of its orientation in inertia space excludes a marked dynamical effect. Control algorithms are porposed to guarantee stability of the relevant motions of the body when the control parameters are subject to constraints. The efficiency of these solutions is confirmed by modelling experiments.