A geometric approach to single axis time-optimal attitude manoeuvres

Time-optimal manoeuvres are the constrained time optimal slews which enable a spacecraft to attain a desired attitude in minimum time. The distinguishing feature of our work is that we consider arbitrary state transfer on the state space, not necessarily rest to rest manoeuvres. Further we work in a geometric framework, wherein the trajectories are analyzed on a cylinder. This report considers a special case in which the spacecraft is manoeuvering about a single axis, the initial and final orientation as well as momentum are specified. Pontryagin´s maximum principle is applied to characterize the time optimal control map under control constraints. Initially, we consider rest to rest manoeuvres and later this is generalised to any given initial and final values of the momentum.