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Periodic oscillating satellites in the problem of three bodies

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Literatur

  1. Collected Works, 6, p. 229–324.

  2. Paper read before the Am. Math. Soc., June 28 (1900); abstract in Bull. Am. Math. Soc., 7 (1900), p. 12.

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  3. Les Méthodes Nouvelles de la Mécanique Céleste, 1, p. 159.

  4. Recherches Numériques concernant des Solutions Périodiques d'un Cas Spécial du Problème des Trois Corps, Astronomische Nachrichten, Nos. 3230, 3251 (1894).

  5. Sur une Classe de Solutions Périodiques dans un Cas Spécial du Problème des Trois Corps, Bull. Astronomique, 12 (1895), pp. 329–352. The analysis of this paper is apparently vitiated by assuming that the equation which defines the solutions is solvable by series in the square root of one of its parameters. The practical construction of the solutions in the derived form can not be carried out.

  6. Periodic Orbits, Acta Math., 27 (1897), pp. 99–242.

  7. Monthly Notices of the Royal Astronomical Society, 63 (1903), p. 436 and 64 (1908), p. 98.

  8. The first example of the use of an integral for these purposes appears in a paper by the writer, A Class of Periodic Solutions of the Problem of three Bodies with application to the Lunar Theory, Trans. Am. Math. Soc., 7 (1906), pp. 537–577; and the development of an indicated integral for these purposes was first made by the writer and Professor W. D. MacMillan in a paper, as yet unpublished, on periodic infinitesimal satellite orbits when the finite bodies move in ellipses.

  9. Les Méthodes Nouvelles de la Mécanique Céleste, I, p. 58.

  10. On the Solutions of Certain Types of Linear Differential Equations with Periodic Coefficients, Am. J. of Math., 33 (1911), pp. 63–96.

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  11. The fact that the exponents differ in sign depends upon the particular form on the differential equations. See Les Méthodes Nouvelles de la Mécanique Céleste, I, p. 193.

  12. Moulton and MacMillan, loc. cit. § 5.

  13. Moulton and MacMillan, loc. cit. § 15.

  14. F. R. Moulton: The Problem of the Spherical Pendulum from the Standpoint of Periodic Solutions. Rend. Circ. Mat. Pal., 32 (1911), pp. 338–364.

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  15. Paper by Moulton and MacMillan, loc. cit., where the method of constructing the solutions is explained.

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  1. Chicago, USA

    F. R. Moulton

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  1. F. R. Moulton
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Research Associate of the Carnegie Institution of Washington.

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Moulton, F.R. Periodic oscillating satellites in the problem of three bodies. Math. Ann. 73, 441–479 (1913). https://doi.org/10.1007/BF01455953

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