Symbolic-numeric investigation of the aerodynamic forces influence on satellite dynamics

Abstract

An approach for symbolic-numeric stability analysis of equilibrium orientations of a satellite in a circular orbit under the influence of gravitational and aerodynamic forces is considered. The stationary motions of a satellite are governed by a system of nonlinear algebraic equations. A computer algebra method based on an algorithm for the construction of a Groebner basis and the resultant concept is proposed for determining all equilibrium orientations of a satellite with a given aerodynamic torque and given principal central moments of inertia. It is shown that equilibrium orientations are determined by real solutions of algebraic equation of the twelfth degree. Evolution of domains with a fixed number of equilibria is investigated in detail. The stability analysis of equilibria is performed on the basis of Lyapunov theorem. The equilibrium orientations and their stability are analyzed numerically. © 2011 Springer-Verlag.