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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2005, Volume 45, Number 9, Pages 1606–1629
(Mi zvmmf598)
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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.
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
Linking options:
https://www.mathnet.ru/eng/zvmmf598 https://www.mathnet.ru/eng/zvmmf/v45/i9/p1606
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Abstract page: | 295 | Full-text PDF : | 105 | References: | 47 | First page: | 1 |
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