Investigation of equilibria stability conditions of the satellite subject to gravitational and aerodynamic torques. General case

Dynamics of attitude motion of a satellite moving along a circular orbit under influence of gravitational and aerodynamic torques is investigated. A symbolic-numerical method for determining all equilibrium orientations of the satellite in the orbital coordinate system with given aerodynamic torque and given principal central moments of inertia is proposed. Conditions of equilibria existence are obtained depending on four dimensionless parameters of the system. For each equilibrium orientation sufficient conditions of stability are obtained as a result of analysis of generalized energy integral used as Lyapunov’s function. Investigation of domains where stability conditions take place is provided in detail depending on four dimensionless parameters of the problem. It is shown that the number of stable equilibria of the satellite in general case changes from 4 to 2 with the increasing the absolute value of aerodynamic torque.