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Chaos in the N-Body Problem of Stellar Dynamics

  • Douglas C. Heggie
Part of the NATO ASI Series book series (NSSB, volume 272)

Abstract

Stellar dynamics uses several different models of stellar systems, but in this paper we consider the most fundamental, which is governed by the N-body equations:
$$\ddot r_i = - G\sum\limits_{j = 1,j \ne i}^N {m_j \frac{{r_i - r_j }}{{\left| {r_i - r_j } \right|^3 }}} $$
(1)
Stellar dynamics shares these equations with celestial mechanics (a term which is used here to denote the study of the orbital dynamics of bodies in the solar system), but there are important differences of emphasis. In stellar dynamics all masses are comparable, whereas in celestial mechanics one mass tends to dominate (either the sun or a primary). This has an effect on the methods used and the types of motion which result. Approximate analytical methods are of immense value in celestial mechanics, but not in stellar dynamics, where numerical methods predominate. In celestial mechanics motions tend to be very nearly regular for long intervals of time, whereas in stellar systems motions are highly irregular.

Keywords

Globular Cluster Celestial Mechanic Star Cluster Stellar System Close Encounter 
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

  • Douglas C. Heggie
    • 1
  1. 1.Department of MathematicsUniversity of EdinburghEdinburghUK

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