Abstract
The behaviour of three gravitationally interacting particles in a plane, which approach each other almost on a central configuration, is studied. Linearization near a Lagrangean solution and matching methods lead to the following results: (i) After a close triple encounter in the planar problem of three bodies, one particle generally escapes with an arbitrarily large asymptotic velocity. (ii) Particular cases of actual triple collisions may be extended by the method of Easton.
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Chazy, J.: 1922,Ann. Sci. École Norm. Sup. (3)39, 29–130.
Cole, J.: 1968,Perturbation Methods in Applied Mathematics, Blaisdell Publ. Co.
Easton, R.: 1971,J. Diff. Equ. 10, 92–99.
Mather, J. and McGehee, R.: 1975, ‘Solutions of the Collinear Four-Body Problem which become Unbounded in Finite Time’, in J. Moser (ed.)Lecture Notes in Physics 38, 573–597, Springer Verlag.
McGehee, R.: 1974,Invent. Math. 27, 191–227.
McGehee, R.: 1975, ‘Triple Collision in Newtonian Gravitational Systems’, in J. Moser (ed.),Lecture Notes in Physics 38, 550–572, Springer Verlag.
Siegel, C. L.: 1941,Ann. Math. 42, 127–168.
Siegel, C. L.: 1967,Lectures on the Singularities of the Three-Body Problem, Tata Institute, Bombay.
Szebehely, V.: 1974,Astron. J. 79, 1449–1454.
Waldvogel, J.: 1972,Celes. Mech. 6, 221–231.
Waldvogel, J.: 1975,Celes. Mech. 11, 429–432.
Waldvogel, J.: 1976, ‘Triple Collision’, in V. Szebehely and B. Tapley (eds),Long Time Prediction in Dynamics, D. Reidel Publ. Co., Dordrecht-Holland.
Wintner, A.: 1941,Analytical Foundations of Celestial Mechanics, Princeton University Press.
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Waldvogel, J. The three-body problem near triple collision. Celestial Mechanics 14, 287–300 (1976). https://doi.org/10.1007/BF01228513
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DOI: https://doi.org/10.1007/BF01228513