Libration points of a gyrostat in a generalized restricted three-body problem: Linear stability

In this paper we consider the dynamics, in some invariant manifolds of the motion of a gyrostat in Newtonian attraction with two. spherical rigid bodies (or material points), by means of a Hamiltonian function that generalizes the planar restricted three-body problem. We obtain three collinear (or Eulerian) equilibria for the restricted planar three body problem with a gyrostat. The triangular (or Lagrangian) equilibria have been completely determined and their linear stability region and resonance curves are given. The classical result of the planar restricted three-body problem is obtained as a particular case. Similar results are given for the Hill lunar problem with a gyrostat.