Abstract
A method is introduced to regularize binary collisions between one of the bodies and any number of other bodies in the three-dimensional problem ofn-bodies. The coordinates are first transformed from an inertial system to a system relative to one of the bodies. The KS dependent variable transformation and a new independent variable transformation are introduced for the regularization.
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Aarseth, S. J.: 1971,Astrophys. Space Sci. 14, 118.
Aarseth, S. J. and Zare, K.: 1974, this issue, p. 185.
Baumgarte, J. and Stiefel, E.: 1974, in D. G. Bettis (ed.),Lecture Notes in Mathematics, Springer Verlag, Heidelberg, Vol. 362, p. 207.
Bettis, D. G. and Szebehely, V.: 1971,Astrophys. Space Sci. 14, 133.
Kustaanheimo, P. and Stiefel, E.: 1965,J. Reine Angew. Math. 218, 204.
Levi-Civita, T.: 1903,Ann. Math. 9, 1.
Nacozy, P. E.: 1972,AIAA J. 10, 704.
Peters, C. F.: 1968,Bull. Astron. 3, 167.
Stiefel, E.: 1970,Celes. Mech. 2, 274.
Stiefel, E. and Scheifele, G.: 1971,Linear and Regular Celestial Mechanics, Springer-Verlag, Berlin Heidelberg, New York.
Szebehely, V.: 1967,Theory of Orbits, Academic Press, New York.
Szebehely, V. and Bettis, D. G.: 1971,Astrophys. Space Sci. 13, 365.
Szebehely, V., Pierce, D. A., and Standish, E. M.: 1964,AIAA Progr. Astron. Aeron. 14, 35.
Whittacker, E. T.: 1904,Analytical Dynamics, Cambridge University Press.
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Zare, K. A regularization of multiple encounters in gravitationalN-body problems. Celestial Mechanics 10, 207–215 (1974). https://doi.org/10.1007/BF01227620
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DOI: https://doi.org/10.1007/BF01227620