Tiscareno, M.S., Burns, J.A., and Thomas, P.C. (2008). "The Rotation of Janus and Epimetheus." American Astronomical Society, DDA meeting #39, #13.03.


Abstract
The rotation states of the Saturnian moons Janus and Epimetheus experience a perturbation every four years, as the moons swap orbits. The sudden change in the orbital rate produces a free libration about synchronous rotation that is subsequently damped by internal friction. Because both moons (especially Epimetheus) are significantly triaxial, their rotational dynamics are controlled by the torque on the moon's figure, rather than the torque on any Saturn-raised tidal bulge. The free libration is fast, with a frequency on the order of the orbital frequency. The damping is therefore also fast, perhaps several months for Janus but less than that for Epimetheus. The quick libration frequency also results in a small libration amplitude, with the long axis differing by only a fraction of a degree from the sub-Saturn point, which is well below the current limits for detection by Cassini Imaging.

Janus and Epimetheus also have small orbital eccentricities which give rise to forced librations about their synchronous rotation states. For Janus, the forced libration is even smaller in amplitude than the free libration. For Epimetheus, the forced libration amplitude is several degrees, approaching the limits of detectability. Measurement of this forced libration would place a constraint on the moon's moments of inertia, as has been done for Mars' Phobos.