We numerically investigate the dynamics of orbits in 3D circumbinary phase-space as a function of binary eccentricity and mass fraction. We find that inclined circumbinary orbits in the elliptically-restricted three-body problem display a nodal libra
tion mechanism in the longitude of the ascending node and in the inclination to the plane of the binary. We (i) analyse and quantify the behaviour of these orbits with reference to analytical work performed by Farago & Laskar (2010) and (ii) investigate the stability of these orbits over time. This work is the first dynamically aware analysis of the stability of circumbinary orbits across both binary mass fraction and binary eccentricity. This work also has implications for exoplanetary astronomy in the existence and determination of stable orbits around binary systems.
