  In this paper the non-canonical Hamiltonian dynamics of a gyrostat in the
three body problem will be examined. By means of geometric-mechanics methods
some relative equilibria of the dynamics of a gyrostat in Newtonian interaction
with two rigid bodies will be studied. Taking advantage of the results obtained
in previous papers, working on the reduced problem, the bifurcations of these
relative equilibria will be studied. The instability of Eulerian relative
equilibria if the gyrostat is close to a sphere is proven. Necessary and
sufficient conditions will be provided for lineal stability of Lagrangian
relative equilibria if the gyrostat is close to a sphere. The analysis is done
in vectorial form avoiding the use of canonical variables and the tedious
expressions associated with them. In this way, the classic results on
equilibria of the three-body problem, many of them obtained by other authors
who had used of more classic techniques, are generalized.
