Optimal attitude control with two rotation axes

Euler proved that every rotation of a 3-dimensional body can be realized as a sequence of three rotations around two given axes. If we allow sequences of an arbitrary length, such a decomposition will not be unique. In this paper we solve an optimal control problem minimizing the total angle of rotation for such sequences. We determine the list of possible optimal patterns that give a decomposition of an arbitrary rotation. Our results may be applied to the attitude control of a spacecraft with two available axes of rotation.