Wobble of a spin stabilized satellite with cross products of inertia and magnetic attitude control

Asymmetrical spin stabilized satellite dynamics in the vicinity of the required motion is considered. The principal axis of the maximum moment of inertia slightly deviates from its assumed direction in the satellite reference frame. This is formalized in the cross products of inertia. This inertial uncertainty results in a wobble, that is undesired angular velocity components perpendicular to the rotation axis, and oscillations of this axis near the required direction. The torque-free motion is investigated first. Expressions that explicitly relate satellite inertia parameters to wobble are provided. Wobble evolution under the action of magnetic damping control is analyzed next. Its amplitude approximate exponential decay behavior and residual unavoidable wobble level are derived. These expressions are compared with numerical simulation results of nonlinear equations of motion including various disturbance sources.