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Zh. Vychisl. Mat. Mat. Fiz., 2005, Volume 45, Number 9, Pages 1606–1629 (Mi zvmmf598)  

This article is cited in 2 scientific papers (total in 2 papers)

An asymptotic solution to the bounded plane circular three body problem

A. E. El'bert

Institute of Mathematics and Mechanics, Ural Division, Russian Academy of Sciences, ul. S. Kovalevskoi 16, Yekaterinburg, 620219, Russia

Abstract: The motion of a mass point in the gravitational field of two bodies traveling in circular orbits about their center of mass is considered. The mass ratio of the two bodies is equal to $\varepsilon\ll 1$. When the mass point passes close to the smaller mass, the character of its trajectory changes abruptly, and the trajectory asymptotics as $\varepsilon\to 0$ is complex. A uniform asymptotic expansion of the entire trajectory accurate to any power of $\varepsilon$ is constructed and validated. In particular, an algorithm is presented for finding the limiting turning angle of the trajectory after the mass point passes near the smaller mass.

Key words: three body problem, asymptotic expansions, solution matching.

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English version:
Computational Mathematics and Mathematical Physics, 2005, 45:9, 1549–1572

Bibliographic databases:
UDC: 519.6:517.933
Received: 29.03.2005

Citation: A. E. El'bert, “An asymptotic solution to the bounded plane circular three body problem”, Zh. Vychisl. Mat. Mat. Fiz., 45:9 (2005), 1606–1629; Comput. Math. Math. Phys., 45:9 (2005), 1549–1572

Citation in format AMSBIB
\Bibitem{Elb05}
\by A.~E.~El'bert
\paper An asymptotic solution to the bounded plane circular three body problem
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2005
\vol 45
\issue 9
\pages 1606--1629
\mathnet{http://mi.mathnet.ru/zvmmf598}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2216072}
\zmath{https://zbmath.org/?q=an:1088.70008}
\transl
\jour Comput. Math. Math. Phys.
\yr 2005
\vol 45
\issue 9
\pages 1549--1572


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. El'bert A.E., “Asymptotic solution of the restricted bounded three-body problem with a mass point moving near a small-mass body”, Doklady Mathematics, 74:2 (2006), 640–643  crossref  mathscinet  zmath  isi  scopus
    2. El'bert A., “Asymptotic solution to the restricted three-body problem with a mass point moving near a small-mass body”, Math Methods Appl Sci, 33:15 (2010), 1807–1849  crossref  mathscinet  zmath  adsnasa  isi  scopus
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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