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Treatment of Close Approaches in the Numerical Integration of the Gravitational Problem of N Bodies

  • D. G. Bettis (a1) and V. Szebehely (a1)

Abstract

One of the main difficulties encountered in the numerical integration of the gravitational n-body problem is associated with close approaches. The singularities of the differential equations of motion result in losses of accuracy and in considerable increase in computer time when any of the distances between the participating bodies decreases below a certain value. This value is larger than the distance when tidal effects become important, consequently, numerical problems are encountered before the physical picture is changed. Elimination of these singularities by transformations is known as the process of regularization. This paper discusses such transformations and describes in considerable detail the numerical approaches to more accurate and faster integration. The basic ideas of smoothing and regularization are explained and applications are given.

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References

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Aarseth, S.: 1970, this issue, p. 20.
Bettis, D. G. : 1970, Numer. Math. 14, 421434.
Fehlberg, E.: 1968, NASA TR R-287, also 1969, Computing 4, 93.
Heggie, D.: 1970, this issue, p. 35.
Henrici, P. : 1962, Discrete Variable Methods in Ordinary Differential Equations, John Wiley and Sons.
Hurwitz, A.: 1933, Math. Werke, Vol. 2, Birkhauser, Basel.
Kustaanheimo, P. and Stiefel, E.: 1965, J. Math. 218, 204.
Levi-Civita, T.: 1903, Ann. Math. 9, 1.
Peters, C. F.: 1968, Bull. Astron. 3, 167.
Schubart, J. and Stumpff, P.: 1966, Veröff. Astron. Rechen-Inst. Heidelberg, No. 18, Karlsruhe.
Stiefel, E. and Bettis, D. G.: 1969, Numer. Math. 13, 15475.
Stiefel, E. and Scheifele, G.: 1970, Linear and Regular Celestial Mechanics, Springer-Verlag.
Sundman, K. F.: 1912, Acta Math. 35, 105.
Szebehely, V.: 1967, Theory of Orbits, Academic Press, New York.
Szebehely, V.: 1968, Bull. Astron. 3, 91.
Szebehely, V. and Bettis, D. G.: 1970, Astrophys. Space Sci. 13, 365.

Treatment of Close Approaches in the Numerical Integration of the Gravitational Problem of N Bodies

  • D. G. Bettis (a1) and V. Szebehely (a1)

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