Satellite dynamics due to gravity and constant torques

We consider the dynamics of the rotational motion of a satellite moving in the central Newtonian force field in a circular orbit due to gravity and constant torques. We propose a method for determining all positions of equilibrium (equilibrium orientations) of a satellite in the orbital coordinate system given the values of the vector of constant torque and the major central moments of inertia; we obtained the conditions for the existence of these positions. We classify the domains with an equal number of equilibrium positions using algebraic methods for the construction of discriminant hypersurfaces. The results obtained in this study can be used to construct gravitational control systems for the orientation of artificial Earth satellites.