Detumbling and nutation canceling maneuvers with complete analytic reduction for axially symmetric spacecraft

A new method is introduced to control and analyze the rotational motion of an axially symmetric rigid-body spacecraft. In particular, this motion is seen as the combination of the rotation of a virtual sphere with respect to the inertial frame, and the rotation of the body, about its symmetry axis, with respect to this sphere. Two new exact solutions are introduced for the motion of axially symmetric rigid bodies subjected to a constant external torque in the following cases: (1) torque parallel to the angular momentum and (2) torque parallel to the vectorial component of the angular momentum on the plane perpendicular to the symmetry axis. By building upon these results, two rotational maneuvers are proposed for axially symmetric spacecraft: a detumbling maneuver and a nutation canceling maneuver. The two maneuvers are the minimum time maneuvers for spherically constrained maximum torque. These maneuvers are simple and elegant, as they reduce the control of the three degrees-of-freedom nonlinear rotational motion to a single degree-of-freedom linear problem. Furthermore, the complete (both for the dynamics and for the kinematics) and exact analytic solutions are found for the two maneuvers. An extended survey is reported in the introduction of the paper of the few cases where the rotation of a rigid body is fully reduced to an exact analytic solution in closed form.