  Optimal control problems are formulated and efficient computational
procedures are proposed for attitude dynamics of a rigid body with symmetry.
The rigid body is assumed to act under a gravitational potential and under a
structured control moment that respects the symmetry. The symmetry in the
attitude dynamics system yields a conserved quantity, and it causes a
fundamental singularity in the optimal control problem. The key feature of this
paper is its use of computational procedures that are guaranteed to avoid the
numerical ill-conditioning that originates from this symmetry. It also
preserves the geometry of the attitude dynamics. The theoretical basis for the
computational procedures is summarized, and examples of optimal attitude
maneuvers for a 3D pendulum are presented.
