The Spin–Spin Problem in Celestial Mechanics

We study the dynamics of two homogeneous rigid ellipsoids subject to their mutual gravitational influence. assume that spin axis each ellipsoid coincides with its shortest physical and is perpendicular orbital plane. Due such assumptions, problem planar depends on particular parameters ellipsoids, most notably, equatorial oblateness flattening respect axes. consider models for configuration: while in full model, there a coupling between rotational motions, Keplerian centers mass bodies are constrained move coplanar ellipses. The case, approximation includes spins what we call spin-spin problem, generalization classical spin-orbit problem. In this paper continue investigations [Mis21] by comparing it also model. Beside detailing associated problems, introduce notions standard balanced resonances, which lead us investigate existence periodic quasi-periodic solutions. give qualitative description phase space provide results linear stability solutions problems. conclude providing comparison reference interaction motions.