Abstract. A software system elaborated on the basis of the computer algebra software package "Mathematica" has been employed in investigations of stability of a relative equilibrium position for an uncontrolled satellite having a gravitation stabilizer on a circular orbit. Domains of various degrees of Poincaré instability have been revealed in the space of introduced parameters. Under the assumption that the potential system is unstable (the degree of instability being even) the problem of possibility of its gyroscopic stabilization is considered. Parametric analysis of stability conditions has been conducted and two-parameter sections of the system domains of gyroscopic stabilization have been constructed with the aid of an applied program intended for graphic representation of the solution of the system of algebraic inequalities.