On the relative equilibria of a satellite-gyrostat, their branchings and stability

The set of relative equilibria of a satellite-gyrostat in a Newtonian gravitational field is studied. The simple geometrical form of this set is described. The branching and stability of the equilibria of a symmetric gyrostat are considered. The results are represented by bifurcation diagrams, on which the degree of stability of the equilibria is distributed in accordance with a law whereby the stability changes at a fixed value of the gyrostatic moment.