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Russia Moscow
Year
2020
Volume
30
Issue
4
Pages
657-671
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Section Mechanics
Title On normal coordinates in the vicinity of the Lagrangian libration points of the restricted elliptic three-body problem
Author(-s) Markeev A.P.ab
Affiliations Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciencea, Moscow Aviation Instituteb
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
UDC 531.1, 521.1
MSC 70H15, 70F07
DOI 10.35634/vm200409
Received 12 May 2020
Language Russian
Citation Markeev A.P. On normal coordinates in the vicinity of the Lagrangian libration points of the restricted elliptic three-body problem, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2020, vol. 30, issue 4, pp. 657-671.
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