  This paper provides a comprehensive analysis of stability and long-time
behaviour of a coupled system constituted by two rigid bodies separated by a
thin layer of lubricant. We show that permanent rotations of the whole system,
with the solids at relative rest, are exponentially stable if and only if the
axis of rotation is the principal axis of inertia corresponding to the largest
moment of inertia of the outer body. All other equilibria are normally
hyperbolic, and hence unstable. In addition, we show that all solutions to the
governing equations converge to an equilibrium configuration, no matter which
initial conditions are chosen. Numerical evidence of the above results as well
as conditions ensuring attainability of the stable configurations are also
presented. For the stability analysis we use a linearization principle for
dynamical systems possessing a center manifold. The characterization of the
long-time behaviour is obtained by a careful analysis of the partially
dissipative system of equations governing the motion of the coupled system.
