Application of Computer Algebra Methods to Investigation of Influence of Constant Torque on Stationary Motions of Satellite

Abstract

Methods of computer algebra are used to study the properties of a nonlinear algebraic system that determines equilibrium orientations of a satellite moving along a circular orbit under the action of gravitational and constant torques. An algorithm for the construction of a Groebner basis is proposed for determining the equilibrium orientations of a satellite with a given constant torque and given principal central moments of inertia. The number of equilibria depending on the parameters of the problem is found by the analysis of real roots of algebraic equation of degree 6 from constructed Groebner basis. The domains with different numbers of equilibria are specified by the discriminant hyper surface given by discriminant of 6 degree polynomial, which was computed symbolically. The equations of boundary curves of two-dimensional section of the discriminant hypersurface are determined in function of values of the components of constant torque. Classification of domains with different number of equilibria from 24 to 0 is carried out for arbitrary values of the parameters.