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Preprints of the Keldysh Institute of Applied Mathematics, 2019, 079, 18 pp.
DOI: https://doi.org/10.20948/prepr-2019-79 (Mi ipmp2717) 		 
The newest methods of celestial mechanics

A. D. Bruno
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DOI: https://doi.org/10.20948/prepr-2019-79
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.
  • Method of normal forms, allowing to study regular perturbations near a stationary solution, near a periodic solution and so on.
  • Method of truncated systems, found with a help of the Newton polyhedrons, allowing to study singular perturbations.
  • Method of generating families of periodic solutions (regular and singular).
  • Method of generalized problems, allowing bodies with negative masses.
  • 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.
Funding agency Grant number
Russian Foundation for Basic Research 18–01–00422_а
Bibliographic databases:
Document Type: Preprint
UDC: 517.93+531.314
Language: Russian
Citation: A. D. Bruno, “The newest methods of celestial mechanics”, Keldysh Institute preprints, 2019, 079, 18 pp.
Citation in format AMSBIB
\Bibitem{Bru19}
\by A.~D.~Bruno
\paper The newest methods of celestial mechanics
\jour Keldysh Institute preprints
\yr 2019
\papernumber 079
\totalpages 18
\mathnet{http://mi.mathnet.ru/ipmp2717}
\crossref{https://doi.org/10.20948/prepr-2019-79}
\elib{https://elibrary.ru/item.asp?id=39174198}
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    		Препринты Института прикладной математики им. М. В. Келдыша РАН
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