Numerical Experiments on the N-Body Problem

  • S. J. Aarseth
Part of the Astrophysics and Space Science Library book series (ASSL, volume 31)


This review first discusses the different types of numerical methods available for integrating the equations of motion of N-body systems. It is desirable to supplement ordinary integration schemes with special treatments of close encounters using a two-body perturbation description or introducing regularizing transformations of the co-ordinates and time. Direct methods are at present limited to the study of a few hundred particles but larger systems may be investigated using Monte Carlo techniques or the Boltzmann moment equations.

N-body computations have been performed for a whole range of initial conditions and the general results are summarized. Numerical investigations have already clarified a number of important aspects of cluster evolution and the qualitative behaviour of small stellar systems is now quite well understood. Recent theoretical modifications have reduced the disagreement with experiments but further improvements are still needed.


Particle Number Star Cluster Escape Rate Halo Orbit Close Encounter 
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  1. Aarseth, S. J.: 1966, Monthly Notices Roy. Astron. Soc. 132, 35.ADSGoogle Scholar
  2. Aarseth, S. J.: 1967, Bull. Astron. 2, 47.Google Scholar
  3. Aarseth, S. J.: 1968, Bull. Astron. 3, 105.Google Scholar
  4. Aarseth, S. J.: 1970, Astron. Astrophys. 9, 64.ADSzbMATHGoogle Scholar
  5. Aarseth, S. J.: 1972, this volume, p. 373.Google Scholar
  6. Albada, T. S. van: 1968, Bull Astron. Inst. Neth. 19, 479.ADSGoogle Scholar
  7. Allen, C.: 1968, Ph.D. Thesis, Mexico University.Google Scholar
  8. Bouvier, P. and Janin, G.: 1972, this volume, p. 71.Google Scholar
  9. Gonzalez, C. C. and Lecar, M.: 1968, Bull. Astron. 3, 209.Google Scholar
  10. Hayli, A.: 1967, Bull. Astron. 2, 67.Google Scholar
  11. Hayli, A.: 1970, Astron. Astrophys. 7, 17.ADSGoogle Scholar
  12. Heggie, D. C.: 1972, this volume, p. 148.Google Scholar
  13. Hénon, M.: 1966, Compt. Rend. Acad. Sci. Paris 262, 666.Google Scholar
  14. Hénon, M.: 1969, Astron. Astrophys. 2, 151.ADSGoogle Scholar
  15. Hénon, M.: 1972, this volume, p. 44.Google Scholar
  16. Hoerner, S. von: 1960, Z. Astrophys. 50, 184.MathSciNetADSzbMATHGoogle Scholar
  17. Hoerner, S. von: 1963, Z. Astrophys. 57, 47.ADSzbMATHGoogle Scholar
  18. Kustaanheimo, P. and Stiefel, E.: 1965, Math. 218, 204.MathSciNetzbMATHGoogle Scholar
  19. Larson, R. B.: 1970, Monthly Notices Roy. Astron. Soc. 147, 323.ADSGoogle Scholar
  20. Larson, R. B.: 1972, this volume, p. 60.Google Scholar
  21. Miller, R. H.: 1964, Astrophys. J. 140, 250.ADSCrossRefGoogle Scholar
  22. Peters, C. F.: 1968, Bull. Astron. 3, 167.Google Scholar
  23. Pines, S.: 1961, Astron. J. 66, 5.MathSciNetADSCrossRefGoogle Scholar
  24. Standish, E. M.: 1968, Ph.D. Thesis, Yale University.Google Scholar
  25. Standish, E. M. and Aksnes, K.: 1969, Astrophys. J. 158, 519.ADSCrossRefGoogle Scholar
  26. Stiefel, E.: 1967, NASA Report CR-769.Google Scholar
  27. Wielen, R.: 1967, Veröff. Astron. Rechen-Inst. Heidelberg,No. 19.Google Scholar
  28. Widen, R.: 1968, Bull. Astron. 3, 127.Google Scholar
  29. Wielen, R.: 1972, this volume, p. 62.Google Scholar

Copyright information

© D. Reidel Publishing Company, Dordrecht, Holland 1972

Authors and Affiliations

  • S. J. Aarseth
    • 1
  1. 1.Institute of Theoretical AstronomyCambridgeEngland

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