 | | 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: | | 12854 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4810 |
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| << Previous article | Volume 55, Issue 8 / 2020 | Next article >> |
| Markeev A.P., "Subharmonic Oscillations in the Near-Circular Elliptic Sitnikov Problem," Mech. Solids. 55 (8), 1162-1171 (2020) |
| Year |
2020 |
Volume |
55 |
Number |
8 |
Pages |
1162-1171 |
| DOI |
10.3103/S0025654420080154 |
| Title |
Subharmonic Oscillations in the Near-Circular Elliptic Sitnikov Problem |
| Author(s) |
Markeev A.P. (Ishlinsky Institute for Problems in Mechanics of the RAS, Moscow, Russia; Moscow Aviation Institute, Moscow, Russia, anat-markeev@mail.ru) |
| Abstract |
We have considered the case of a restricted three-body problem (material points), when the
masses of the two main attracting bodies are equal. Their orbits have been assumed to be ellipses. The
problem regarding the third body’s motion of negligible mass under the influence of the main body’s
gravitational attraction (the Sitnikov problem) allows particular solutions for the following: the third
body moves along a straight line passing through the center of mass of the main bodies and perpendicular to the plane of their orbits. We have assumed that the eccentricity of the main body orbits is small
and we investigated the nonlinear problem of the existence of the third body’s periodic motion with a
period multiple of the revolution period of the main bodies in their orbits. The problem of stability (in
Lyapunov’s sense) of these periodic motions under both perturbations keeping the trajectory of the
third body rectilinear and arbitrary spatial perturbations has also been solved. |
| Keywords |
restricted three-body problem, subharmonic oscillations, stability |
| Received |
03 April 2020 | Revised |
22 May 2020 | Accepted |
25 May 2020 |
| Link to Fulltext |
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