An efficient method for studying the stability and dynamics of the rotational motions of celestial bodies

We use the alternative MEGNO (Mean Exponential Growth of Nearby Orbits) technique developed by Cincotta and Simó to study the stability of orbital—rotational motions for plane oscillations and three-dimensional rotations. We present a detailed numerical—analytical study of a rigid body in the case where the proper rotation of the body is synchronized with its orbital motion as 3: 2(Mercurian—type synchronism). For plane rotations, the loss of stability of the periodic solution that corresponds to a 3: 2 resonance is shown to be soft, which should be taken into account to estimate the upper limit for the ellipticity of Mercury. In studying stable and chaotic translational—rotational motions, we point out that the MEGNO criterion can be effectively used. This criterion gives a clear picture of the resonant structures and allows the calculations to be conveniently presented in the form of the corresponding MEGNO stability maps for multidimensional systems. We developed an appropriate software package.