 | | 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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| Bryuno A.D., "Modern Methods of Celestial Mechanics," Mech. Solids. 56 (1), 84-94 (2021) |
| Year |
2021 |
Volume |
56 |
Number |
1 |
Pages |
84-94 |
| DOI |
10.3103/S0025654421010052 |
| Title |
Modern Methods of Celestial Mechanics |
| Author(s) |
Bryuno A.D. (Keldysh Institute of Applied Mathematics Russian Academy of Sciences, Moscow, 125047 Russia, abruno@keldysh.ru) |
| Abstract |
In connection with the 120th anniversary of the publication of the last volume of A. Poincaré’s book "New Methods of Celestial Mechanics", the following methods are considered that have arisen since then.
1. The normal form method, which allows one to study regular perturbations near a stationary solution, near a periodic solution, etc.
2. The method of truncated systems obtained with the help of Newton polyhedra, which allows the study of singular perturbations.
3. The method of generating families of periodic solutions (regular and singular).
4. Method of generalized problems admitting bodies with negative masses.
5. Calculation of the network of families of periodic solutions as a “skeleton” of a part of the phase space. |
| Keywords |
Hamiltonian system, normal form, truncated Hamiltonian, family of periodic solutions, generating family, negative mass, skeleton |
| Received |
06 December 2019 | Revised |
11 December 2019 | Accepted |
19 December 2019 |
| Link to Fulltext |
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