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Transactions of the American Mathematical Society

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Permanent configurations in the $ n$-body problem


Author: Carl Holtom
Journal: Trans. Amer. Math. Soc. 54 (1943), 520-543
MSC: Primary 85.0X
DOI: https://doi.org/10.1090/S0002-9947-1943-0008951-6
MathSciNet review: 0008951
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  • [1] H. Andoyer, Sur l'équilibre relatif de $ n$-corps, Bulletin Astronomique vol. 23 (1906) pp. 50-59.
  • [2] Emilia Breglia, Su alcuni casi particolari del problema dei tre corpi, Giornale de Mathematiche (3) vol. 7 (1916) pp. 151-173.
  • [3] O. Dziobek, Über einen merkwürdigen Fall des Vielkörperproblems, Astronomische Nachrichten vol. 152 (1900) pp. 33-46.
  • [4] L. Euler, Theoria motuum planetarum et cometarum, 1744.
  • [5] L. Euler, De motu rectilineo trium corporum se mutuo attrahentium, Novi Commentarii Academiae Scientiarum Imperialis Petropolitanae vol. 11 (1776); Considérations sur le Problème des trois corps, Mémoirs de l'Académie des Sciences de Berlin 1763 (1770) pp. 194-220.
  • [6] J. J. L. Hinrichsen, Bounds for the libration points in a restricted problem of $ n$-bodies, Bull. Amer. Math. Soc. vol. 48 (1942) p. 45.
  • [7] R. Hoppe, Erweiterung der bekannten Speziallösung des dreikörper Problems, Archiv der Mathematik und Physik vol. 64 (1879) pp. 218-233.
  • [8] J. L. Lagrange, Essai sur le problème des trois corps, Œ uvres vol. 6 (1772) pp. 229-324.
  • [9] R. Lehmann-Filhès, Über zwei Fälle des vielkörper Problems, Astronomische Nachrichten vol. 127 (1891) pp. 137-144.
  • [10] W. R. Longley, Some particular solutions in the problem of $ n$-bodies, Bull. Amer. Math. Soc. vol. 13 (1906-1907) pp. 324-335. MR 1558474
  • [11] W. D. MacMillan, Dynamics of rigid bodies, 1936.
  • [12] W. D. MacMillan and W. Bartky, Permanent configurations in the problem of four bodies, Trans. Amer. Math. Soc. vol. 34 (1932) pp. 838-875. MR 1501666
  • [13] F. R. Moulton, Straight line solutions in the problem of $ n$-bodies, Ann. of Math. (2) vol. 12 (1910) pp. 1-17. MR 1503509
  • [14] Newton, Principia, book one, §2, 3d ed., 1725.
  • [15] F. Tisserand, Mécanique céleste, vol. 1, 1889, chap. 8.
  • [16] W. L. Williams, Permanent configurations in the problem of five bodies, Trans. Amer. Math. Soc. vol. 44 (1938) pp. 562-579. MR 1501982
  • [17] A. Wintner, Analytical foundation of celestial mechanics, 1941. MR 0005824 (3:215b)

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DOI: https://doi.org/10.1090/S0002-9947-1943-0008951-6
Article copyright: © Copyright 1943 American Mathematical Society

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