  We investigate the motion, near the equilibrium configurations, of an
initially spinless rigid body subject to an external tidal field. Two cases are
considered: when the center of mass of the body is at rest at the equilibrium
point of the field generated by a generic mass distribution, and when it is
placed on a circular orbit subject to a spherically symmetric potential. A
complete analysis of the equilibrium configurations is carried out for both
cases. First, we derive the conditions for the stable equilibria, and then we
analyze the frequencies of oscillations around the equilibrium positions. In
view of these results, we consider the problem of alignment of galaxies in
clusters. After estimating the period of the oscillations induced on the
galaxies by the tidal field of the cluster, we discuss the possible effect of
resonances between stellar orbits inside the galaxy and the oscillations of the
galaxy as a whole; this may be a mechanism responsible for producing an
intracluster stellar population.
