Abstract
The use of regularization methods based on the Kustaanheimo-Stiefel transformation (KS) is reviewed. The history of the development of such methods is summarized and anecdotal information about the related events is told. Details of the multi-particle regularization methods are given, including the most recent developments.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aarseth, S. J.: 1971, āBinary Evolution in Stellar Systemsā, Astrophys. Space Sci. 13, 324.
Aarseth, S. J.: 1972, āDirect Integration Methods of the N-body Problemā, in Gravitational N-body Problem, proceedings of IAU colloquium No. 10, ed. M. Lecar, Reidel, Dordrecht, pp.373ā387.
Aarseth, S. J.: 1974, āDynamical Evolution of Simulated Star Clusterrs. I. Isolated Modelsā, Astron. Astrophys., 35, 237.
Aarseth, S. J.: 1977, Rev. ŠŠµŃ . Astron. Astrofis., 3, 199.
Aarseth, S. J.: 1988, āIntegration Methods for Small N-Body Systemsā,p. 287ā306, in The Few Body Problem, (Valtonen M. J., ed.), Kluwer, Dordrecht, Holland.
Aarseth, S. J. 1996, āStar cluster simulations on HARPā,p. 161ā170, in Dynamical Evolution of Star Clusters, ed. Hut, P. and Makino, J., Kluwer.
Aarseth, S. J. and Zare, K.: 1974, āA Regularization of the Three-Body Problemā, Cel. Mech., 10, 185ā205.
Aarseth, S. J. and Heggie, D. C: 1976, āThe Probability of Binary Formation by Three-Body Encountersā, Astron. Astrophys., 53, 259ā265.
van Albada, T. S.: 1968, āThe evolution of small stellar systems and its implications for the formation of double starsā, Bull. astr. Inst. Neth., 20, 57.
Alexander, M. E.: 1986, āSimulations of binary-single star and binary-binary scatteringā, J. Comp. Phys., 64, 195ā219.
Bulirsch, R. and Stoer, J.: 1966, āNumerical Treatment of Differential Equations by Extrapolation Methodsā, Num. Math., 8, 1ā13.
Heggie, D. C: 1974, āA Global Regularisation of the Gravitational N-Body Problemā, Cel. Mech., 10, 217ā241.
Heggie, D. C.: 1988, āThe N-Body Problem in Stellar Dynamicsā, in Long-Term Dynamical Behaviour of Natural and Artificial N-Body Systems, (Roy A. E., ed.), 329ā347, Kluwer, Dordrecht, Holland.
von Hoerner, S.: 1960, Z. Astrophys. 50, 184.
von Hoerner, S.: 1963, Z. Astrophys. 57, 47.
Hopf, H. 1931, āUber die Abbildung der dreidimensionalen SphƤre auf die KugelflƤcheā, Math. Ann. 104. Reprinted in: Selecta Heinz Hopf, 38ā63, Springer 1964.
Kustaanheimo, P.: 1964, āDie Spinordarstellung der energetischen IdentitƤten der Kepler-bewegungā, p. 333ā340. In: E. Stiefel (ed.): Mathematische Methoden der Himmelsmechanik und Astronautik, Mathematisches Forschungsinstitut Oberwolfach, Berichte 1. Bibliographisches Institut Mannheim, 1966, 350 pp.
Kustaanheimo, P. and Stiefel, E.: 1965, āPerturbation theory of Kepler motion based on spinor regularizationā, J. Reine Angew. Math., 218, 204ā219.
Levi-Civita, T.: 1920, āSur la rĆ©gularisation du problĆØme des trois corpsā, Acta Math. 42, 99ā144.
Mikkola, S.: 1983, āEncounters of Binaries ā I. Equal Energiesā, Mon. Not. R. Astr. Soc, 203, 1107ā1121.
Mikkola, S.: 1985, āA Practical and Regular Formulation of the N-Body Equationsā, Mon. Not. R. Astr. Soc, 215, 171ā177.
Mikkola, S. and Aarseth, S. J.: 1990, āA Chain Regularization Method for the Few-Body Problemā, Cel. Mech., 47, 375ā390.
Mikkola, S. and Aarseth, S. J.: 1993, āAn Implementation of N-body Chain Regularizationā, Celest. Mech. Dyn. Astron. 57, 439
Mikkola, S. and Aarseth, S. J.: 1996, āA Slow-Down Treatment of Close Binariesā, Celest. Mech. Dyn. Astron. (to appear).
Stiefel, E. L. and Scheifele, G.: 1971, Linear and Regular Celestial Mechanics, Springer, Berlin.
Szebehely, V.: 1967, Theory of Orbits, Academic Press, New York.
Szebehely, V. and Bettis, D. G. 1972, in Gravitational N-body Problem, proceedings of IAU colloquium No. 10, ed. M. Lecar, Reidel, Dordrecht, pp. 136ā147.
Szebehely, V. and Peters, C. F.: 1967, āComplete solution of a general problem of three bodiesā, Astron. J., 72, 876.
Szebehely, V. and Zare, K: 1975, āTime transformations in the extended phase-spaceā, Cel. Mech., 11, 469.
Waldvogel, J.: 1972, āA new regularization of the planar problem of three bodiesā, Cel. Mech., 6, 221.
Waldvogel, J., Kirchgraber, U. Schwarz, H. R, Henrici, P.: 1979, āIn Memoriam E. Stiefel.ā ZAMP 30, 133ā142.
Zare, K.: 1974, āA Regularization of Multiple Encounters in Gravitational N-body Problemsā Cel. Mech., 10, 207ā215.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
Ā© 1997 Kluwer Academic Publishers
About this chapter
Cite this chapter
Mikkola, S. (1997). Numerical Treatment of Small Stellar Systems with Binaries. In: Docobo, J.A., Elipe, A., McAlister, H. (eds) Visual Double Stars: Formation, Dynamics and Evolutionary Tracks. Astrophysics and Space Science Library, vol 223. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-1477-3_33
Download citation
DOI: https://doi.org/10.1007/978-94-009-1477-3_33
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-7161-1
Online ISBN: 978-94-009-1477-3
eBook Packages: Springer Book Archive