Dynamics at intermediate angular invariant

Determine the dynamical behaviors of the Kirchhoff equations for the Aref–Jones ellipsoid at intermediate values of the angular invariant between the pure and planar landmark solutions.

Background

The numerical exploration focuses primarily on trajectories with angular invariant near its maximal value, near zero, or exactly zero. The authors explicitly identify the region between the pure modes, for which the angular and linear momenta are nearly aligned, and the planar modes, for which the angular invariant vanishes, as largely unexplored. A complete investigation would identify the regular, chaotic, and connecting behaviors occurring at general intermediate angular-invariant values.