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A Journal of Russian Academy of Sciences
in January 1966
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IssuesArchive of Issues2021-1pp.84-94

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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,
Abstract In connection with the 120th anniversary of the publication of the last volume of A. Poincarés 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 2019Revised 11 December 2019Accepted 19 December 2019
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