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Orbits asymptotic to the straight line equilibrium points in the problem of the three finite bodies. (English) JFM 48.1077.01

Auch im Falle endlicher Massen gibt es nach Lagrange eine Lösung des Dreikörperproblems, bei der die drei Körper als starre Figur auf einer Geraden bleiben. Der Verf. weist Lösungen auf, die sich dieser Lagrangeschen Lösung mit wachsender Zeit unbegrenzt nähern. Ein Zahlenbeispiel wird durchgerechnet und gezeichnet.

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[1] Ch.Lagrange,Oeuvres complètes, (Paris, Gauthier-Villars), vol. VI, pp. 229–324;P. Tisserand,Traité de Mécanique céleste, t. I (Paris, Gauthier-Villars, 1889), Chap. VIII;F. R. Moulton,Introduction to Celestial Mechanics (New York, Mac Millan, 1914), pp. 309–318.
[2] H. Poincaré,Les Méthodes nouvelles de la Mécanique céleste, t. I (Paris, Gauthier-Villars, 1892), Chap. VII.
[3] L. A. H. Warren,A class of Asymptotic Orbits in the Problem of Three Bodies [American Journal of Mathematics, vol. XXXVIII (1916), pp. 221–248]. · JFM 46.1380.03
[4] D. Buchanan,Asymptotic Satelites near the Straight-Line Equilibrium Points in the Problem of Three Bodies [American Journal of Mathematics, vol. XLI (1919), pp. 79–110]. · JFM 47.1007.02
[5] F. R. Moulton,Periodic Orbits (Washington, Carnegie Institution, 1920), Chap. V. · JFM 47.0836.02
[6] D. Buchanan,Asymptotic Satellites near Equilateral. Triangle Equilibrium Points in the Problem of Three Bodies [Transactions of the Cambridge Philosophical Society, vol. XXII, No. XV (1919), pp. 309–340]. · JFM 47.0838.01
[7] Chap. IX of Moulton’sPeriodic Orbits, loc. 7).
[8] D. Buchanan,Orbits Asymptotic to an Isosceles-Triangle Solution of the Problem of Three Bodies [Proceedings of the London Mathematical Society, Series II, vol. XVII, Part 1, pp. 54–74].
[9] D. Buchanan, Chap. X ofMoulton’s Periodic Orbits, 1. c. 7).
[10] A determination of the straight line equlibrium points to which the preceding is somewhat similar may be found in any treatise on Celestial Mechanics, but seeMoulton’s Introduction to Celestial Mechanics, l. c. 2), pp. 309–312.
[11] 1. c. 4), p. 340.
[12] 1. c. 4), p. 341.
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