The rotation of Mercury

The planet Mercury is currently the target of two space missions: MESSENGER (NASA) which performed two fly-bys last year, and Bepi-Colombo (ESA/JAXA), scheduled to be launched in 2014. In the framework of the preparation of Bepi-Colombo, we elaborate a short-term theory of the rotation of Mercury, in considering that the planet is composed of a spherical liquid core and a rigid mantle. The rotation of Mercury is a unique case in the Solar System, because it is locked in a 3:2 spin-orbit resonance. Unfortunately, this is nearly the only observed indication on Mercury's rotation, except some recent radar data seeming to reveal a liquid core. We start from an Hamiltonian formalism and use both analytical (Lie transforms) and numerical tools (numerical integrations, frequency analysis,...). this is an opportunity to compare the advantages and drawbacks of the two methods. Our results consist in a description of the forced longitudinal and latitudinal librations due to planetary perturbations. We also highlight two possible resonances that raise the amplitudes of some librations.