
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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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
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\paper An asymptotic solution to the bounded plane circular three body problem
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\yr 2005
\vol 45
\issue 9
\pages 16061629
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\zmath{https://zbmath.org/?q=an:1088.70008}
\transl
\jour Comput. Math. Math. Phys.
\yr 2005
\vol 45
\issue 9
\pages 15491572
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This publication is cited in the following articles:

El'bert A.E., “Asymptotic solution of the restricted bounded threebody problem with a mass point moving near a smallmass body”, Doklady Mathematics, 74:2 (2006), 640–643

El'bert A., “Asymptotic solution to the restricted threebody problem with a mass point moving near a smallmass body”, Math Methods Appl Sci, 33:15 (2010), 1807–1849

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