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Description
We investigate the small-time local controllability of a nonlinear control-affine system modeling the rotational motion of a satellite on a circular orbit, focusing on an underactuated scenario where the control torque is generated solely by magnetorquers. The satellite is treated as a rigid body subject to electromagnetic actuation. The main contributions include establishing small-time local controllability around the relative equilibrium under natural assumptions on the mass distribution of the rigid body. This is achieved using the Lie algebra rank condition and Sussmann's controllability condition. The study also reveals that the linearized system is not controllable in a neighborhood of the equilibrium. Hence, the presented research contributes to the advancement of essentially nonlinear controllability theory for dynamical systems with drift.
