Several Problems on Rejecting Disturbances Acting on Rigid Spacecraft

Motivated by existing literatures, several problems on rejecting disturbances acting on rigid spacecraft are studied in this paper for the first time. A theorem is proposed to evaluate a lower bound of the maximum Euclidean norm of the angular velocity. The theorem is proved by contradiction. Mainly based on this theorem, the following questions on rejecting disturbances are studied for the first time: 1) whether can spacecraft attitude and angular velocity be made to tend to zero in the presence of bounded disturbances either by using a control input vector that, after some time, becomes relatively small, or by using a control input vector that tends to zero? 2) At least how large should each component of the control input vector be authorized to reject bounded disturbances? 3) What characters should the control input vector have to reject an arbitrary disturbance? The answers to these questions give some facts on rejecting disturbances. Before designing a control algorithm to reject disturbances, it is better to know these facts