 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 11262 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8011
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| In English (Mech. Solids): | | 3251 |
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| A.P. Markeev, "On the Stability of Lagrange Solutions in the Spatial Near-Circular Restricted Three-Body Problem," Mech. Solids. 56 (8), 1541-1549 (2021) |
| Year |
2021 |
Volume |
56 |
Number |
8 |
Pages |
1541-1549 |
| DOI |
10.3103/S0025654421080124 |
| Title |
On the Stability of Lagrange Solutions in the Spatial Near-Circular Restricted Three-Body Problem |
| Author(s) |
A.P. Markeev (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, 119526 Russia;Moscow Aviation Institute, Moscow, 125993 Russia, anat-markeev@mail.ru) |
| Abstract |
The restricted problem of three bodies (material points) is considered. The orbits of the
main attracting bodies are assumed to be ellipses of small eccentricity, and the passively gravitating
body during its motion can leave the plane of the orbits of the main bodies (spatial problem). The stability of body motion corresponding to triangular Lagrangian libration points is investigated. A characteristic feature of the spatial problem under study is the presence of resonance due to the equality of
the Keplerian motion period of the main bodies and the linear oscillation period of the passively gravitating body in the direction perpendicular to the plane of their orbits. Using the methods of classical
perturbation theory, Kolmogorov—Arnold—Moser (KAM) theory and computer algebra algorithms,
the nonlinear problem of stability for most (in the Lebesgue-measure sense) initial conditions and formal stability (stability in any arbitrarily high finite approximation with respect to the coordinates and
impulses of perturbed motion) are investigated. |
| Keywords |
restricted three-body problem, triangular libration points, stability |
| Received |
15 January 2021 | Revised |
11 March 2021 | Accepted |
15 March 2021 |
| Link to Fulltext |
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