Abstract: A control system for providing attitude control in spacecraft. The control system comprising a primary attitude reference system, a secondary attitude reference system, and a hyper-complex number differencing system. The hyper-complex number differencing system is connectable to the primary attitude reference system and the secondary attitude reference system.

Abstract: An attitude control system and method operative with a thruster controls the attitude of a vehicle carrying the thruster, wherein the thruster has a valve enabling the formation of pulses of expelled gas from a source of compressed gas. Data of the attitude of the vehicle is gathered, wherein the vehicle is located within a force field tending to orient the vehicle in a first attitude different from a desired attitude. The attitude data is evaluated to determine a pattern of values of attitude of the vehicle in response to the gas pulses of the thruster and in response to the force field. The system and the method maintain the attitude within a predetermined band of values of attitude which includes the desired attitude. Computation circuitry establishes an optimal duration of each of the gas pulses based on the pattern of values of attitude, the optimal duration providing for a minimal number of opening and closure operations of the valve.