The software SONYR acronym for "Spin-Orbit Relativistic N-body model" was developed to highlight the spin-orbit coupling. This software allows to treat the whole body of the Solar System and to calculate their effects on orbit and rotation of Mercury. A set of free libration (called eigen libration periods of 16 to 1066 years) and forced libration (period of 88 days) were calculated. Scientists have shown that the average obliquity of Mercury is 1.6 seconds of arc, and this value is adopted for a planet Mercury in the Cassini state. For more information: see Rambaux and Bois (2004).
Scientists at the ROB and FUNDP (Facultés Universitaires Notre Dame de la Paix) also built an analytical model of Mercury's rotation and identified the possible states of equilibrium and in particular, the balance in which Mercury is present ( 3:2 resonance). They also study the effects of depreciation, the planetary perturbations on the rotation of Mercury, and representations in phase space (a way to represent the trajectories of evolution, the amount of movement, according to all possibilities for positions and velocities). For more information: see d'Hoedt, Lemaître, and Rambaux (2006), Lemaître, d'Hoedt and Rambaux (2006) and Rambaux, Lemaître, and d'Hoedt (2007).