Resonance rotation of celestial bodies and Cassini's laws

Celestial body rotation about its center of mass, taking into account the body orbit evolution, is considered. Non-linear evolution equations of motion are constructed. Empirical Cassini's laws describing the Moon motion result from these equations as their stationary points. Bifurcation conditions of steady motions are written out and conditions of their stability are investigated. Hypothesis of Mercury's resonance motion analogous to the motion by Cassini is discussed. Consequences of this hypothesis are considered.The first information including the results mentioned in the paper was previously published in preprint 1].