Steady motions of an axisymmetric satellite: An atlas of their bifurcations

The steady motions of an axially symmetric rigid satellite orbiting a fixed spherically symmetric rigid body are considered in this paper. Based on a model for the dynamics of the satellite which incorporates the classical approximation for the gravitational potential and includes the attitude-orbit coupling, the bifurcations and non-linear stability of the steady motions of the satellite are discussed. These results extend earlier works on this problem by Likins, Pringle, Rumyantsev, Stepanov, and Thomson, by showing how the motions found by these authors are interrelated, and how several of them are physically unrealistic because their orbital radii are too small.