The Lidov-Kozai mechanism allows a body to periodically exchange its
eccentricity with inclination. It was first discussed in the framework of the
quadrupolar secular restricted three-body problem, where the massless particle
is the inner body, and later extended to the quadrupolar secular nonrestricted
three body problem. In this paper, we propose a different point of view on the
problem by looking first at the restricted problem where the massless particle
is the outer body. In this situation, equilibria at high mutual inclination
appear, which correspond to the population of stable particles that Verrier &
Evans (2008,2009) find in stable, high inclination circumbinary orbits around
one of the components of the quadruple star HD 98800. We provide a simple
analytical framework using a vectorial formalism for these situations. We also
look at the evolution of these high inclination equilibria in the non
restricted case.Comment: 11 pages, 6 figures. Accepted by MNRAS 2009 September 1