  The Saturnian coorbital satellites Janus and Epimetheus present a unique
dynamical configuration in the Solar System, because of high-amplitude
horseshoe orbits, due to a mass ratio of order unity. As a consequence, they
swap their orbits every 4 years, while their orbital periods is about 0.695
days. Recently, Tiscareno et al.(2009) got observational informations on the
shapes and the rotational states of these satellites. In particular, they
detected an offset in the expected equilibrium position of Janus, and a large
libration of Epimetheus. We here propose to give a 3-dimensional theory of the
rotation of these satellites in using these observed data, and to compare it to
the observed rotations. We consider the two satellites as triaxial rigid
bodies, and we perform numerical integrations of the system in assuming the
free librations as damped. The periods of the three free librations we get,
associated with the 3 dimensions, are respectively 1.267, 2.179 and 2.098 days
for Janus, and 0.747, 1.804 and 5.542 days for Epimetheus. The proximity of
0.747 days to the orbital period causes a high sensitivity of the librations of
Epimetheus to the moments of inertia. Our theory explains the amplitude of the
librations of Janus and the error bars of the librations of Epimetheus, but not
an observed offset in the orientation of Janus.
