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KIAM Preprint  79, Moscow, 2019
Authors: Bruno A. D.
The newest methods of celestial mechanics
Abstract:
The last volume of the book Les méthods nouvelles de la mecanique céleste by Poincaré was published 120 years ago. Since then, the following methods have arisen. 1. Method of normal forms, allowing to study regular perturbations near a stationary solution, near a periodic solution and so on. 2. Method of truncated systems, found with a help of the Newton polyhedrons, allowing to study singular perturbations. 3. Method of generating families of periodic solutions (regular and singular). 4. Method of generalized problems, allowing bodies with negative masses. 5. Computation of a net 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, generated family, negative mass, skeleton
Publication language: russian,  pages: 18
Research direction:
Mathematical modelling in actual problems of science and technics
Russian source text:
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About authors:
  • Bruno Alexander Dmitrievich,  orcid.org/0000-0002-7465-1258KIAM RAS