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Predictability, Stability, and Chaos in N-Body Dynamical Systems pp 47–62Cite as

Chaos in the N-Body Problem of Stellar Dynamics

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Part of the book series: NATO ASI 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.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Edinburgh, Edinburgh, UK

    Douglas C. Heggie

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  1. Douglas C. Heggie
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Editor information

Editors and Affiliations

  1. University of Glasgow, Glasgow, UK

    Archie E. Roy

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© 1991 Plenum Press, New York

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Heggie, D.C. (1991). Chaos in the N-Body Problem of Stellar Dynamics. In: Roy, A.E. (eds) Predictability, Stability, and Chaos in N-Body Dynamical Systems. NATO ASI Series, vol 272. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-5997-5_4

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  • DOI: https://doi.org/10.1007/978-1-4684-5997-5_4

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4684-5999-9

  • Online ISBN: 978-1-4684-5997-5

  • eBook Packages: Springer Book Archive

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