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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
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.
Received: 12.05.2020
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
Linking options:
https://www.mathnet.ru/eng/vuu748 https://www.mathnet.ru/eng/vuu/v30/i4/p657
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