  This paper presents sufficient conditions for small-time local
controllability of a control-affine system that describes the rotational motion
of a satellite in a circular orbit. The satellite is modeled as a rigid body
subject to electromagnetic actuation. We focus on the underactuated scenario
where the control torque is generated solely by magnetorquers. The main
contributions of this work include proving small-time local controllability
around the relative equilibrium under some natural assumptions on the mass
distribution of the rigid body. This result is based on the Lie algebra rank
condition and Sussmann's controllability condition. Furthermore, it is shown
that the linearized system is not controllable in a neighborhood of the
considered equilibrium.
