Hostname: page-component-77c89778f8-7drxs Total loading time: 0 Render date: 2024-07-17T15:02:50.336Z Has data issue: false hasContentIssue false
  • English
  • Français

Direct Integration Methods of the N-Body Problem

Published online by Cambridge University Press:  12 April 2016

S. J. Aarseth
S. J. Aarseth*
Affiliation:
Institute of Theoretical Astronomy, Cambridge, England

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A fourth-order polynomial method for the integration of N-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.

Type
Research Article
Information
International Astronomical Union Colloquium , Volume 10: Gravitational N-Body Problem , November 1971 , pp. 118 - 132
Copyright
Copyright © Reidel 1971

References

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