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Fundam. Prikl. Mat., 2000, Volume 6, Issue 1, Pages 249–263 (Mi fpm470)  

This article is cited in 2 scientific papers (total in 2 papers)

Reduction of the two-body problem with central interaction on simply connected surfaces of a constant curvature

A. V. Shchepetilov

M. V. Lomonosov Moscow State University

Abstract: The problem of two particles with central interaction on simply connected surfaces of a constant curvature was considered. Due to the absence in this case of the Galileo transformation, it's reduction to the one particle problem was carried out by Marsden–Weinstein method. The classification of reduced dynamic systems was given. For two of them the conditions of the global solution existence for dynamic equations with attractive potentials were found. The comparison of the structure of obtained Hamiltonians with integrals of one particle problem with Bertrand's potentials was carried out.

Full text: PDF file (637 kB)

Bibliographic databases:
UDC: 531.01
Received: 01.03.1997

Citation: A. V. Shchepetilov, “Reduction of the two-body problem with central interaction on simply connected surfaces of a constant curvature”, Fundam. Prikl. Mat., 6:1 (2000), 249–263

Citation in format AMSBIB
\Bibitem{Shc00}
\by A.~V.~Shchepetilov
\paper Reduction of the~two-body problem with central interaction on simply connected surfaces of a~constant curvature
\jour Fundam. Prikl. Mat.
\yr 2000
\vol 6
\issue 1
\pages 249--263
\mathnet{http://mi.mathnet.ru/fpm470}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1798149}
\zmath{https://zbmath.org/?q=an:1003.70006}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Maciejewski, AJ, “Non-integrability of restricted two body problems in constant curvature spaces”, Regular & Chaotic Dynamics, 8:4 (2003), 413  crossref  mathscinet  zmath  adsnasa  isi
    2. Shchepetilov, AV, “Nonintegrability of the two-body problem in constant curvature spaces”, Journal of Physics A-Mathematical and General, 39:20 (2006), 5787  crossref  mathscinet  zmath  adsnasa  isi
  • Фундаментальная и прикладная математика
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