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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A reduction of the three body problem by means of transformation groups


Author: James W. Sauve
Journal: Trans. Amer. Math. Soc. 119 (1965), 21-36
MSC: Primary 70.20
MathSciNet review: 0181143
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  • [1] R. Marcolongo, Il problema dei tre corpi, Ulrice Hoepli, Milan, 1919.
  • [2] E. T. Whittaker, A treatise on the analytical dynamics of particles and rigid bodies: With an introduction to the problem of three bodies, 4th ed, Cambridge University Press, New York, 1959. MR 0103613 (21 #2381)
  • [3] Aurel Wintner, The Analytical Foundations of Celestial Mechanics, Princeton Mathematical Series, v. 5, Princeton University Press, Princeton, N. J., 1941. MR 0005824 (3,215b)
  • [4] E. R. Van Kampen and Aurel Wintner, On a Symmetrical Canonical Reduction of the Problem of Three Bodies, Amer. J. Math. 59 (1937), no. 1, 153–166. MR 1507227, http://dx.doi.org/10.2307/2371569
  • [5] L. Pontrjagin, Topological groups, Princeton Univ. Press, Princeton, N. J., 1939.
  • [6] Claude Chevally, Theory of Lie groups, Princeton Univ. Press, Princeton, N. J., 1946.
  • [7] Luigi Bianchi, Lezioni sulla teoria dei gruppi continui finiti di transformazioni, Pisa, 1918.
  • [8] S. Lie and G. Scheffers, Vorlesungen über Differentialgleichungen mit Bekanten Infinitesimalen Transformationen, Teubner, Leipzig, 1891.
  • [9] Lawrence Markus, Quadratic differential equations and non-associative algebras, Contributions to the theory of nonlinear oscillations, Vol. V, Princeton Univ. Press, Princeton, N.J., 1960, pp. 185–213. MR 0132743 (24 #A2580)
  • [10] Abraham Cohen, An introduction to the Lie theory of one-parameter groups, Stechert, New York, 1931. (Original publication, 1911).

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1965-0181143-0
PII: S 0002-9947(1965)0181143-0
Article copyright: © Copyright 1965 American Mathematical Society