Controllability of spacecraft systems in a central gravitational field

The natural configuration space for spacecraft systems in a central gravitational field can be modeled by SO(3)×R³, where the special orthogonal group SO(3) represents the attitude dynamics and R³ is for the orbital dynamics. While the attitude dynamics of the spacecraft system is affected by the orbital elements through the well-known gravity-gradient torque, it has not been noted before, to the authors´ knowledge, that the effects of attitude-orbit coupling can be used to change orbital motions by controlling the attitude. This controllability property is the main issue of this work. The authors prove that the control systems for spacecraft with reaction wheels or gas jets as attitude controllers are controllable