Optimal attitude control of a spinning space-body--A graphical approach

A simplified mathematical model of a rigid, long space-body, spinning at constant rate about an axis of symmetry, is presented. From a heuristic analysis of the vehicle trajectories in the pitch-yaw plane, obtained by application of impulsive control effort, the minimum-fuel two-impulse control law for the case of unlimited thrust is readily deduced. This yields the absolute lower bound on fuel consumption. For the case of limited thrust, based on the minimum-fuel two-impulse control scheme, two suboptimal control laws are determined and illustrated with examples. An approximate graphical construction of the trajectories in the pitch-yaw plane is given, from which the total fuel spent and the total time for control can be evaluated.