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A Brief History of Regularisation

Published online by Cambridge University Press:  01 September 2007

S. Mikkola
S. Mikkola*
Affiliation:
Tuorla Observatory, University of Turku, Väisäläntie 20, Piikkiö, Finland email: [email protected]
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Abstract

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The various methods for regularisation of the gravitational few-body problem, from the coordinate transformation by the Kustaanheimo-Stiefel method to the more recent methods of algorithmic regularisation, are reviewed. Numerical comparisons of the performance of the methods are presented and future research suggested.

Keywords

stellar dynamicsmethods: n-body simulationsmethods: numerical
Type
Contributed Papers
Information
Proceedings of the International Astronomical Union , Volume 3 , Symposium S246: Dynamical Evolution of Dense Stellar Systems , September 2007 , pp. 218 - 227
Copyright
Copyright © International Astronomical Union 2008

References

Aarseth, S. J. 1972, in Gravitational N-body Problem, proceedings of IAU colloquium No. 10, ed. Lecar, M., Reidel, Dordrecht, pp. 373–387.Google Scholar
Aarseth, S. J. 2003, Gravitational N-Body Simulations, Cambridge Univ. Press, CambridgeGoogle Scholar
Aarseth, S. J. & Zare, K. 1974, Celestial Mechanics, 10, 185Google Scholar
Bulirsch, R. & Stoer, J. 1966, Numerical Mathematics, 8, 1Google Scholar
Heggie, D. C. 1974, Celestial Mechanics, 10, 217CrossRefGoogle Scholar
Kustaanheimo, P. & Stiefel, E. 1965, J. Reine Angew. Math., 218, 204Google Scholar
Levi-Civita, T. 1920, Acta Mathematica, 42, 99CrossRefGoogle Scholar
Mikkola, S. 1985, MNRAS, 215, 171Google Scholar
Mikkola, S. & Aarseth, S. J. 1990, Celestial Mechanics and Dynamical Astronomy, 47, 375Google Scholar
Mikkola, S. & Aarseth, S. J. 1993, Celestial Mechanics and Dynamical Astronomy, 57, 439CrossRefGoogle Scholar
Mikkola, S. & Aarseth, S. 2002, Celestial Mechanics and Dynamical Astronomy, 84, 343CrossRefGoogle Scholar
Mikkola, S. & Merritt, D. 2006, MNRAS, 372, 219Google Scholar
Mikkola, S. & Tanikawa, K. 1999a, Celestial Mechanics and Dynamical Astronomy, 74, 287Google Scholar
Mikkola, S. & Tanikawa, K. 1999b, MNRAS, 310, 745CrossRefGoogle Scholar
Preto, M. & Tremaine, S. 1999, AJ, 118, 2532CrossRefGoogle Scholar
Siegel. C. L. 1956, Vorlesungen über Himmelsmechanik, Springer, Berlin-Göttingen-Heidelberg.Google Scholar
Stiefel, E. L. & Scheifele, G. 1971, Linear and Regular Celestial Mechanics, Springer, Berlin.CrossRefGoogle Scholar
Szebehely, V. & Peters, C. F. 1967, AJ, 72, 876.Google Scholar
von Hoerner, S. 1960, Z. Astrophys., 50, 184Google Scholar
von Hoerner, S. 1963, Z. Astrophys., 57, 47Google Scholar
Zare, K. 1974, Celestial Mechanics, 10, 207Google Scholar