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
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.
three body problem, asymptotic expansions, solution matching.
PDF file (2394 kB)
Computational Mathematics and Mathematical Physics, 2005, 45:9, 1549–1572
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
\paper An asymptotic solution to the bounded plane circular three body problem
\jour Zh. Vychisl. Mat. Mat. Fiz.
\jour Comput. Math. Math. Phys.
Citing articles on Google Scholar:
Related articles on Google Scholar:
This publication is cited in the following articles:
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
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
|Number of views:|