| Abstract: |
| The gravitationally interacting three bodies are called hierarchical when their orbits are well approximated by double Kepler orbits which do not intersect each other.
The presence of the mean motion resonances (MMRs), which have overlapped part, contributes the chaotic nature of the system. In highly inclined systems another process comes to the system, called the von Zeipel-Kozai-Lidov (ZKL) oscillation, that is, anti-correlated oscillation between the inner orbitfs eccentricity $e_1$ and mutual inclination $I$. Potentially, a configuration of higher $e_1$ and lower $I$ would lead a close approach and a member-change of hierarchy.
In order to understand how systems lose their hierarchical stability under both the effects of MMRs and the ZKL mechanism, we will carry out a detailed inspection of a single orbit. Introducing three auxiliary quantities about the two outer bodies, which account the closeness, the alignment of two pericenters, and synchronous rotation around the central, we found via timecourse analysis that the ZKL mechanism and secular drift of the pericenters finally broke the hierarchy of the system. |
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