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- Publisher
- Springer Journals
- Copyright
- Copyright © Pleiades Publishing, Ltd. 2021
- ISSN
- 1560-3547
- eISSN
- 1468-4845
- DOI
- 10.1134/s1560354721040018
- Publisher site
- See Article on Publisher Site
Abstract
A study is made of the stability oftriangular libration points in the nearly-circularrestricted three-body problem in the spatial case.The problem of stability for most (in the sense of Lebesguemeasure) initial conditions in the planar casehas been investigated earlier. In the spatial case,an identical resonance takes place: for all values of the parameters of theproblem the period of Keplerian motion of the two mainattracting bodies is equal to the period of small linearoscillations of the third body of negligible massalong the axis perpendicular to the plane of the orbitof the main bodies. In this paper it is assumed that there are no resonances of theplanar problem through order six. Using classical perturbation theory, KAM theoryand algorithms of computer calculations, stability is proved for most initial conditionsand the Nekhoroshev estimate of the time of stability is given for trajectories startingin an addition to the above-mentioned set of most initial conditions.
Journal
Regular and Chaotic Dynamics – Springer Journals
Published: Aug 9, 2021
Keywords: restricted three-body problem; triangular libration points; stability; Arnold diffusion