  The Cassini spacecraft collects high resolution images of the saturnian
satellites and reveals the surface of these new worlds. The shape and rotation
of the satellites can be determined from the Cassini Imaging Science Subsystem
data, employing limb coordinates and stereogrammetric control points. This is
the case for Epimetheus (Tiscareno et al. 2009) that opens elaboration of new
rotational models (Tiscareno et al. 2009; Noyelles 2010; Robutel et al. 2011).
Especially, Epimetheus is characterized by its horseshoe shape orbit and the
presence of the swap is essential to introduce explicitly into rotational
models. During its journey in the saturnian system, Cassini spacecraft
accumulates the observational data of the other satellites and it will be
possible to determine the rotational parameters of several of them. To prepare
these future observations, we built rotational models of the coorbital (also
called Trojan) satellites Telesto, Calypso, Helene, and Polydeuces, in addition
to Janus and Epimetheus. Indeed, Telesto and Calypso orbit around the L_4 and
L_5 Lagrange points of Saturn-Tethys while Helene and Polydeuces are coorbital
of Dione. The goal of this study is to understand how the departure from the
Keplerian motion induced by the perturbations of the coorbital body, influences
the rotation of these satellites. To this aim, we introduce explicitly the
perturbation in the rotational equations by using the formalism developed by
Erdi (1977) to represent the coorbital motions, and so we describe the
rotational motion of the coorbitals, Janus and Epimetheus included, in compact
form.
