Symbolic-Numeric Simulation of Satellite Dynamics with Aerodynamic Attitude Control System

The dynamics of the rotational motion of a satellite, subjected to the action of gravitational, aerodynamic and damping torques in a circular orbit is investigated. Our approach combines methods of symbolic study of the nonlinear algebraic system that determines equilibrium orientations of a satellite under the action of the external torques and numerical integration of the system of linear ordinary differential equations describing the dynamics of the satellite. An algorithm for the construction of a Grobner basis was implemented for determining the equilibria of the satellite for specified values of the aerodynamic torque, damping coefficients, and principal central moments of inertia. Both the conditions of the satellite's equilibria existence and the conditions of asymptotic stability of these equilibria were obtained. The transition decay processes of the spatial oscillations of the satellite for various system parameters have also been studied.