Controllability of an underactuated spacecraft with one thruster under disturbance

For an underactuated spacecraft using only one thruster, the attitude controllability with respect to the or- bit frame is studied in the presence of periodical oscillation disturbance, which provides a preconditional guide on de- signing control law for underactuated attitude control sys- tem. Firstly, attitude dynamic model was established for an underactuated spacecraft, and attitude motion was described using the special orthogonal group （SO （3））. Secondly, Liou- ville theorem was used to confirm that the flow generated by the drift vector of the underactuated attitude control system is volume-preserving. Furthermore, according to Poincar6＇s re- currence theorem, we draw conclusions that this drift field is weakly positively poisson stable （WPPS）. Thirdly, the suffi- cient and necessary condition of controllability was obtained on the basis of lie algebra rank condition （LARC）. Finally, the controllable conditions were analyzed and simulated in different cases of inertia matrix with the installed position of thruster.