Origin of additional oscillations in full spin-spin phase portraits

Determine whether the additional oscillations observed in the projections of solution trajectories to the phase portraits of the full spin-spin problem—i.e., two interacting rigid ellipsoids with coupled rotational and orbital dynamics—originate from the time-variation of the orbital parameters (semimajor axis and eccentricity) induced by the coupling between rotation and orbit in the full spin-spin model.

Background

The paper compares the Keplerian spin-spin model (fixed Keplerian orbit) with the full spin-spin model (orbit coupled to rotational dynamics). Numerical simulations show that higher-order resonant islands present in the Keplerian case are largely destroyed in the full problem, and additional oscillations appear in the phase-space projections of the full system.

The authors explicitly conjecture that these additional oscillations arise from the variations of the orbital parameters when the orbit is coupled to the rotation in the full spin-spin dynamics, highlighting an unresolved question about their origin.