Yoram Lithwick & Smadar Naoz (2011)
Extends Lidov–Kozai theory to an eccentric outer perturber, explaining orbit flips and extreme eccentricity in test particles.
The work generalizes the classical Lidov–Kozai resonance by allowing the distant perturber to have nonzero eccentricity, which qualitatively changes the secular dynamics of a test particle. It highlights new behaviors such as orbital flips between prograde and retrograde motion and the production of very high eccentricities that the standard (quadrupole) Kozai picture cannot capture. This provides a cleaner framework for interpreting extreme eccentricity excitation and inclination changes in hierarchical triples, relevant to scenarios like high-eccentricity migration and the formation of close-in companions. The results help clarify when the usual conserved “Kozai constant” breaks down and how octupole-level effects reshape resonant phase space.
Analytical secular (orbit-averaged) dynamics of a hierarchical three-body system, extending beyond the quadrupole Lidov–Kozai approximation.
Celestial mechanics of hierarchical triples, secular perturbation theory, and the classical Lidov–Kozai resonance.