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Hill-Type Stability and Hierarchical Stability of the General Three-Body Problem

  • Yan-Chao Ge
Part of the NATO ASI Series book series (NSSB, volume 272)

Abstract

Hierarchical stability (HS hereafter) was defined by Walker and Roy (1983) in connection with the Jacobian coordinate system. A dynamical N-body system is held to be HS if, during an interval of time substantially longer than the periods of revolution of the bodies in the system, the following conditions hold:
  1. HS-(A).

    none of the bodies escapes to infinity from the system;

     
  2. HS-(B).

    no dramatic changes occur in any orbit’s size, shape or orientation to the invariable plane of the system;

     
  3. HS-(C).

    ρi < ρj for any i < j; where ρi = |ρi| (i=2,..., N), ρi being the Jacobian vectors which connect the barycentre of the first (i-1) masses and the ith mass.

     

Keywords

Jacobian Vector Synodic Period Invariable Plane Negative Total Energy Outer Mass 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Plenum Press, New York 1991

Authors and Affiliations

  • Yan-Chao Ge
    • 1
  1. 1.Department of Physics and AstronomyThe University of GlasgowGlasgowScotland, UK

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