Dynamics of a satellite subject to gravitational and aerodynamic torques. Investigation of equilibrium positions

Abstract

The rotational dynamics of a satellite moving over a circular orbit under an effect of gravitational and aerodynamic torques is investigated. A method is proposed for determining all equilibrium positions (equilibrium orientations) of a satellite in an orbital coordinate system with given values of an aerodynamic torque vector and principal central moments of inertia; the conditions of their existence are obtained, depending on four dimensionless parameters of the problem. Bifurcation values of parameters are found for which the number of equilibrium orientations changes. The numerical analysis of the evolution of regions of existence of various numbers of equilibrium orientations in the space of dimensionless parameters is carried out. The relationship between the obtained regions of existence and the regions of existence of equilibrium orientations of an axisymmetric satellite is considered. It is shown that the number of equilibrium positions of a satellite does not exceed 24 and cannot be less than 8, in the general case.