Relative equilibria and stability of a gyrostat-satellite when the vector of the gyrostatic moment is parallel to the principal central plane of inertia of the satellite

Dynamics of a gyrostat-satellite moving in central Newtonian force field in a circular orbit is investigated. In the particular case when the vector of the gyrostatic moment is parallel to one of the satellite’s principal central planes of inertia, all equilibrium orientations are determined. Conditions of equilibriums existence are obtained depending on three dimensionless parameters of the system. Detailed investigation of existence domains of various numbers of solutions is carried out. All bifurcational values of parameters at which there is a change of quantity of equilibrium orientations are determined. For each equilibrium orientation sufficient conditions of stability are obtained as a result of the generalized energy integral analysis. Evolution of domains of validity for the stability conditions are studied depending on parameters of the system.