Dynamics of a gyrostat on cylindrical and inclined Eulerian equilibria in the three-body problem

The aim of the present paper is to analyze the roto-translational non-canonical Hamiltonian dynamics of a gyrostat in the frame of the three-body problem. Working on the reduced problem and using geometrical and mechanics methods we describe the Eulerian equilibria and study their bifurcations in the dynamics of a gyrostat in Newtonian interaction with two rigid bodies. Moreover, if the gyrostat form is close to a sphere the linear instability of the Eulerian relative equilibria is stated. Finally, we describe the rotational Poisson dynamics and provide sufficient conditions for the non-linear stability in the Eulerian relative equilibria of cylindrical and inclined type.