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 give the list of possible patterns that describe an optimal decomposition of an arbitrary rotation. Our results may be applied to the attitude control of a spacecraft with two available axes of rotation.

Attitude control, Euler's angles, Lie groups
SIAM Journal on Control and Optimization
School of Mathematics and Statistics

Billig, Y. (2019). Optimal attitude control with two rotation axes. SIAM Journal on Control and Optimization, 57(2), 1068–1093. doi:10.1137/140986438