Satellite dynamics under the influence of gravitational and aerodynamic torques. A study of stability of equilibrium positions

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The dynamics of the rotational motion of a satellite, moving in the central Newtonian force field under the influence of gravitational and aerodynamic torques, is investigated. The paper proposes a method for determining all equilibrium positions (equilibrium orientations) of a satellite in the orbital coordinate system for specified values of aerodynamic torque and the major central moments of inertia; the sufficient conditions for their existence are obtained. For each equilibrium orientation the sufficient stability conditions are obtained using the generalized energy integral as the Lyapunov function. The detailed numerical analysis of the regions where the stability conditions of the equilibrium positions are satisfied is carried out depending on four dimensionless parameters of the problem. It is shown that, in the general case, the number of satellite’s equilibrium positions, for which the sufficient stability conditions are satisfied, varies from 4 to 2 with an increase in the value of the aerodynamic torque magnitude.