Geometric Mechanics Based Modeling of the Attitude Dynamics and

The attitude dynamics of a spacecraft with a variable speed control moment gyroscope (VSCMG), in the presence of external torques and internal inputs, is derived using variational prin-ciples. A complete dynamics model, that relaxes some of the assumptions made in prior literature on control moment gyro-scopes, is obtained. A non-standard VSCMG model, that has an offset between the center of the gimbal axis and the center of the rotor (flywheel) is considered. The dynamics equations show the complex nonlinear coupling between the internal degrees of free-dom associated with the VSCMG and the spacecraft base body’s attitude degrees of freedom. Some of this coupling is induced by the non-zero offset between the gimbal axis and the rotor cen-ter. This dynamics model is then generalized to include the ef-fects of multiple control moment gyroscopes placed in the base body with non-parallel gimbal axes. It is shown that the dynam-ical coupling can improve the control authority on the angular momentum of the base body of the spacecraft using changes in the momentum variables of the VSCMG. Numerical simulations confirm the use of these VSCMGs for attitude control for a given de-tumbling maneuver