2009/09/14 by F. Farago, Francois Farago, Jacques Laskar +1 · 164 citations
Engineering · Physics and Astronomy · #Astro and Planetary Science #Asymmetry #Celestial mechanics #Eccentricity (behavior) #Formalism (music) #Massless particle #Point (geometry) #Point particle #Population #Pulsars and Gravitational Waves Research #Spacecraft Dynamics and Control #Three-body problem #astro-ph.EP
paper · pdf · doi:10.1111/j.1365-2966.2009.15711.x
published in Monthly Notices of the Royal Astronomical Society 401(2), 1189-1198 (Oxford University Press) · 11 pages, 6 figures. Accepted by MNRAS 2009 September 11
arxiv created 2009/09/14 · openalex publication_date 2009/11/03 · arxiv updated 2015/05/14 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The Lidov–Kozai mechanism allows a body to periodically exchange its eccentricity with inclination. It was first discussed in the framework of the quadrupolar secular restricted three-body problem, where the massless particle is the inner body, and later extended to the quadrupolar secular non-restricted three-body problem. In this paper, we propose a different point of view on the problem by looking first at the restricted problem where the massless particle is the outer body. In this situation, equilibria at high mutual inclination appear, which corresponds to the population of stable particles that Verrier & Evans find in stable, high-inclination circumbinary orbits around one of the components of the quadruple star HD 98800. We provide a simple analytical framework using a vectorial formalism for these situations. We also look at the evolution of these high-inclination equilibria in the non-restricted case.