A Symbolic Investigation of the Influence of Aerodynamic Forces on Satellite Equilibria

Computer algebra methods 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 aerodynamic torques. An algorithm for the construction of a Grobner basis is proposed for determining the equilibrium orientations of a satellite with given principal central moments of inertia and given aerodynamic torque in special cases, when the center of pressure of aerodynamic forces is located in one of the principal central planes of inertia of the satellite. The conditions of the equilibria existence are obtained, depending on three dimensionless parameters of the problem. The number of equilibria depending on the parameters is found by the analysis of real roots of algebraic equations from the constructed Grobner basis. The evolution of domains with fixed number of equilibria from 24 to 8 is investigated in detail. All bifurcation values of the system parameters corresponding to the qualitative change of these domains are determined.