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Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2020, Volume 30, Issue 4, Pages 657–671
DOI: https://doi.org/10.35634/vm200409
(Mi vuu748)
 

This article is cited in 3 scientific papers (total in 4 papers)

MECHANICS

On normal coordinates in the vicinity of the Lagrangian libration points of the restricted elliptic three-body problem

A. P. Markeevab

a Moscow Aviation Institute (National Research University), Volokolamskoe shosse, 4, Moscow, 125080, Russia
b Ishlinsky Institute for Problems in Mechanics, Russian Academy of Science, pr. Vernadskogo, 101/1, Moscow, 119526, Russia
Full-text PDF (205 kB) Citations (4)
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Abstract: A planar restricted elliptic three-body problem is considered. The motions close to the triangular libration points are studied. The problem parameters (the eccentricity of the orbit of the main attracting bodies and the ratio of their masses) are assumed to lie inside the linear stability region of the libration points. The magnitude of eccentricity is considered small. A linear canonical, periodic in true anomaly transformation is obtained analytically up to the second degree of eccentricity inclusive that reduces the Hamiltonian function of the linearized equations of perturbed motion to real normal form in the vicinity of the libration points. This form corresponds to two harmonic oscillators not connected to one another, with frequencies depending on the problem parameters. In constructing the normalizing canonical transformation, the Depri–Hori method of the perturbation theory of Hamiltonian systems is used. Its implementation in the problem under study relies heavily on computer systems of analytical calculations.
Keywords: three-body problem, orbit eccentricity, triangular libration points, Hamiltonian system, canonical transformation.
Funding agency Grant number
Russian Science Foundation 19-11-00116
The work is carried out at the cost of the grant of the Russian Scientific Foundation (project no. 19-11-00116) at the Moscow Aviation Institute (National Research University) and at the Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Science.
Received: 12.05.2020
Bibliographic databases:
Document Type: Article
UDC: 531.1, 521.1
MSC: 70H15, 70F07
Language: Russian
Citation: A. P. Markeev, “On normal coordinates in the vicinity of the Lagrangian libration points of the restricted elliptic three-body problem”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 30:4 (2020), 657–671
Citation in format AMSBIB
\Bibitem{Mar20}
\by A.~P.~Markeev
\paper On normal coordinates in the vicinity of the Lagrangian libration points of the restricted elliptic three-body problem
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2020
\vol 30
\issue 4
\pages 657--671
\mathnet{http://mi.mathnet.ru/vuu748}
\crossref{https://doi.org/10.35634/vm200409}
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  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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    Abstract page:205
    Full-text PDF :155
    References:26
     
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