The set of relative equilibria of a stationary orbital asymmetric gyrostat

Under consideration is the well-known problem of relative equilibria (an equilibrium position in the orbital coordinate system) of a gyrostat satellite and their dependence on the design parameters. A new geometric approach to the analysis of the set of relative equilibria is developed. It is proposed to determine the relative equilibria in the corresponding three-dimensional Euclidean space using special aggregated parameters of the system by the coordinates of the intersection points of two pairs of corresponding hyperbolic cylinders with the sphere of the unit radius. It is shown that, for arbitrary values of the gyrostatic moment and other parameters of the system, there are at least eight different relative equilibria.