  In this work, we study the dynamics of rotation of the small satellites
Methone and Aegaeon and revisit previous works on the rotation of Prometheus,
Metis, and Amalthea. In all cases, the surfaces of section computed with the
standard spin-orbit model reveal that the synchronous regime with small
amplitude of libration shares another large domain in the phase space. We
reproduce and apply the hamiltonian theory given in Wisdom (2004) to
analytically characterize the detected structure as being a secondary resonance
where the period of oscillation of the physical libration is similar to the
orbital period of the satellite. We also show that the amplitude of libration
around the secondary resonance is always larger than in the case of the other
mode. Since the current rotational states of these sorts of satellites should
be synchronous, our results can be considered in evolutionary studies of their
rotation.
