Astrophysics and Space Science

, Volume 14, Issue 1, pp 118–132 | Cite as

Direct integration methods of theN-body problem

  • S. J. Aarseth


A fourth-order polynomial method for the integration ofN-body systems is described in detail together with the computational algorithm. Most particles are treated efficiently by an individual time-step scheme but the calculation of close encounters and persistent binary orbits is rather time-consuming and is best performed by special techniques. A discussion is given of the Kustaanheimo-Stiefel regularization procedure which is used to integrate dominant two-body encounters as well as close binaries. Suitable decision-making parameters are introduced and a simple method is developed for regularizing an arbitrary number of simultaneous two-body encounters.


Integration Method Special Technique Arbitrary Number Computational Algorithm Direct Integration 


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  1. Aarseth, S. J.: 1968,Bull. Astron. 3, 105.Google Scholar
  2. Aarseth, S. J.: 1970,Astron. Astrophys. 9, 64.Google Scholar
  3. Bettis, D. G. and Szebehely, V. G.: 1972, this issue, p. 133.Google Scholar
  4. Gonzalez, C. C. and Lecar, M.: 1968,Bull. Astron. 3, 209.Google Scholar
  5. Heggie, D. C.: 1972, this issue, p. 35.Google Scholar
  6. Lecar, M.: 1968,Bull. Astron. 3, 91.Google Scholar
  7. Kustaanheimo, P. and Stiefel, E.: 1965,Math. 218, 204.Google Scholar
  8. Peters, C. F.: 1968,Bull. Astron. 3, 167.Google Scholar
  9. Stiefel, E.: 1967, NASA Report CR-769.Google Scholar
  10. Szebehely, V. G. and Peters, C. F.: 1967,Astron. J. 72, 876.Google Scholar
  11. Wielen, R.: 1967,Veröff. Atron. Rechen-Inst. Heidelberg, No. 19.Google Scholar

Copyright information

© D. Reidel Publishing Company 1971

Authors and Affiliations

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

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