Regular and Chaotic Dynamics
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Regul. Chaotic Dyn.:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

Regular and Chaotic Dynamics, 2013, Volume 18, Issue 6, Pages 703–718
DOI: https://doi.org/10.1134/S1560354713060105 (Mi rcd165) 		 
This article is cited in 12 scientific papers (total in 12 papers)

On Action-angle Coordinates and the Poincaré Coordinates

Jacques Féjozab

a Université Paris-Dauphine – CEREMADE (UMR 7534), Place du Maréchal de Lattre de Tassigny, 75775 Paris Cedex 16, France
b Observatoire de Paris – IMCCE (UMR 8028), 77 avenue Denfert-Rochereau, 75014 Paris, France
Citations (12)
References:
PDF
HTML
DOI: https://doi.org/10.1134/S1560354713060105
Abstract: This article is a review of two related classical topics of Hamiltonian systems and celestial mechanics. The first section deals with the existence and construction of action-angle coordinates, which we describe emphasizing the role of the natural adiabatic invariants "$\oint_\gamma p\,dq$". The second section is the construction and properties of the Poincaré coordinates in the Kepler problem, adapting the principles of the former section, in an attempt to use known first integrals more directly than Poincaré did.
Keywords: Hamiltonian system, Lagrangian fibration, action-angle coordinates, Liouville–Arnold theorem, adiabatic invariants, Kepler problem, two-body problem, Poincaré coordinates, planetary problem, first integral, integrability, perturbation theory.
Funding agency Grant number
Agence Nationale de la Recherche ANR-10-BLAN 0102 DynPDE
The author has been partially supported by the French ANR (projet ANR-10-BLAN 0102 DynPDE).
Received: 30.10.2013
Accepted: 11.11.2013
Bibliographic databases:
Document Type: Article
MSC: 01-01, 37-03, 37C80, 37J35, 70-03, 70H06, 70H15
Language: English
Citation: Jacques Féjoz, “On Action-angle Coordinates and the Poincaré Coordinates”, Regul. Chaotic Dyn., 18:6 (2013), 703–718
Citation in format AMSBIB
\Bibitem{Fej13}
\by Jacques F\'ejoz
\paper On Action-angle Coordinates and the Poincaré Coordinates
\jour Regul. Chaotic Dyn.
\yr 2013
\vol 18
\issue 6
\pages 703--718
\mathnet{http://mi.mathnet.ru/rcd165}
\crossref{https://doi.org/10.1134/S1560354713060105}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3146588}
\zmath{https://zbmath.org/?q=an:1290.01001}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000329108900010}
Linking options:
  • https://www.mathnet.ru/eng/rcd165
  • https://www.mathnet.ru/eng/rcd/v18/i6/p703
    • This publication is cited in the following 12 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Statistics & downloads:
    Abstract page:162
    References:55
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024