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Part of the book series: International Centre for Mechanical Sciences ((CISM,volume 170))

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Abstract

In the restricted circular planar problem of three bodies, two bodies (assumed to be point masses and calles primaries) revolve around their center of mass in circular orbits under the influence of their mutual gravitational attraction. A third body (attracted by the previous two but not influencing their motion) moves in the plane defined by the two revolving bodies. The problem is to determine the motion of this third body, (Szebehely, 1967).

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Bibliography for the Restricted Problem

  • Birkhoff, G.D.,“The restricted problem of three bodies”, Rendiconti de Circolo Matematico di Palermo, Vol. 39, pp. 1–70, (1915).

    Article  Google Scholar 

  • Birkhoff, G.D.,“Sur le problème restreint des trois corps”, Two memoirs, both published in Annali della R. Scuola Normale Superiore di Pisa. The first in series 2, Vol. 4, pp. 267–306 (1935); the second in series 2, Vol. 5, pp. 1–42 (1936).

    Google Scholar 

  • Birkhoff, G.D.,“Dynamical systems with two degrees of freedom”, Trans. Am. Math. Soc., Vol. 18, pp. 199–300 (1919).

    Article  MathSciNet  Google Scholar 

  • Brouwer, D. and G. Clemence, “Methods of Celestial Mechanics”, Academic Press, 1961.

    Google Scholar 

  • Charlier, C.L, C.L.,“Die Mechanik des Himmels”, Leipzig, von Veit & Co., First Vol. 1902, Second Vol. 1907.

    Google Scholar 

  • Darwin, G.H.,“Periodic Orbits”, Acta Math., Vol. 21, pp. 99–242, (1897).

    Article  MATH  MathSciNet  Google Scholar 

  • Goldstein, H, H.,“Classical Mechanics”, Addison-Wesley, (1951).

    Google Scholar 

  • Hill, G.W.,“Researches in the lunar theory”, Am. J. of Math., Vol. 1, pp. 5–26, 129–147, 245–260 (1878).

    Google Scholar 

  • Klose, A.,“Topologische Dynamik der interplanetaren Massen”, Vieteljahrsschrift des Astronomischen Gesellschaft, Vol. 67, pp. 61–102, (1932).

    Google Scholar 

  • Levi-Civita, T., Acta Math., Vol. 42, pp. 99–144 (1919).

    Article  MATH  MathSciNet  Google Scholar 

  • Levi-Civita, T.,“Sur la résolution qualitative du problème restreint de trois corps”, Acta Mathematica, Vol. 30, pp. 305–327. (1906).

    Article  MATH  MathSciNet  Google Scholar 

  • Levi-Civita, T.,“Traiettorie singolari ed urti nel problema ri-stretto dei tre corpi”, Annali di Matematica, Ser. 3, Vol. 9, pp. 1–32, (1904).

    Article  Google Scholar 

  • Levi-Civita, T., Ann. di Mat., Ser. 3, Vol. 5, pp. 221–309, (1901).

    MATH  Google Scholar 

  • Moulton, F.R., Proc. Math Congr., Cambridge, England, Vol. 2, pp. 182–187 (1913); also, Periodic Orbits, Carnegie Inst., Wash. (1920).

    Google Scholar 

  • Poincaré, H.,“Les méthodes nouvelles de la mécanique céleste”, Paris, 1892, 1893, 1899.

    ADS  Google Scholar 

  • Strömgren, E.,“Connaissance actuelle des orbites dans le problè me des trois corps”, Bull. Astr. (2), Vol. 9, pp. 87–130 (1935), and Publ. Kbh. Obs. # 100, pp. 1–44 (1935).

    Google Scholar 

  • Szebehely, V, V.“Theory of orbits”, Academic Press, New York, (1967).

    Google Scholar 

  • Whittaker E.T., “Analytical dynamics”, 4th Edition, Dover, (1944).

    Google Scholar 

  • Wintner, A., “The analytical foundations of celestial mechanics”, Princeton Univ. (1947).

    Google Scholar 

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© 1974 Springer-Verlag Wien

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Szebehely, V. (1974). The Restricted Problem. In: The General and Restricted Problems of Three Bodies. International Centre for Mechanical Sciences, vol 170. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2916-6_2

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  • DOI: https://doi.org/10.1007/978-3-7091-2916-6_2

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-81264-8

  • Online ISBN: 978-3-7091-2916-6

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