Abstract:
A study is made of the stability of triangular libration points in the nearly-circular
restricted three-body problem in the spatial case. The problem of stability for most (in the sense
of Lebesgue measure) initial conditions in the planar case has been investigated earlier. In the
spatial case, an identical resonance takes place: for all values of the parameters of the problem
the period of Keplerian motion of the two main attracting bodies is equal to the period of
small linear oscillations of the third body of negligible mass along the axis perpendicular to the
plane of the orbit of the main bodies. In this paper it is assumed that there are no resonances
of the planar problem through order six. Using classical perturbation theory, KAM theory
and algorithms of computer calculations, stability is proved for most initial conditions and the
Nekhoroshev estimate of the time of stability is given for trajectories starting in an addition to
the above-mentioned set of most initial conditions.
Keywords:
restricted three-body problem, triangular libration points, stability, Arnold diffusion.
This research was carried out within the framework of the state assignment (registration
No. AAAA-A20-120011690138-6) at the Ishlinskii Institute for Problems in Mechanics, RAS, and
at the Moscow Aviation Institute (National Research University).
Citation:
Anatoly P. Markeev, “On the Metric Stability and the Nekhoroshev Estimate of the Velocity of Arnold Diffusion in a Special Case of the Three-body Problem”, Regul. Chaotic Dyn., 26:4 (2021), 321–330
\Bibitem{Mar21}
\by Anatoly P. Markeev
\paper On the Metric Stability and the Nekhoroshev Estimate of the Velocity of Arnold Diffusion in a Special Case of the Three-body Problem
\jour Regul. Chaotic Dyn.
\yr 2021
\vol 26
\issue 4
\pages 321--330
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\crossref{https://doi.org/10.1134/S1560354721040018}
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https://www.mathnet.ru/eng/rcd1118
https://www.mathnet.ru/eng/rcd/v26/i4/p321
This publication is cited in the following 3 articles:
A. P. Markeev, “On Resonance Values of Parameters in the Problem of Stability of Lagrange Solutions in a Restricted Three-Body Problem Close to a Circle”, Mech. Solids, 58:7 (2023), 2531
A. P. Markeev, “On Resonant Values of Parameters in the Problem on the Stability of Lagrangian Solutions in the Near-Circular Restricted Three-Body Problem”, Prikladnaya matematika i mekhanika, 87:4 (2023), 589
“Anatoly Pavlovich Markeev. On the Occasion of his 80th Birthday”, Rus. J. Nonlin. Dyn., 18:4 (2022), 467–472
Citation in format AMSBIB
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