RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Sb.:
Year:
Volume:
Issue:
Page:
Find






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


Mat. Sb., 2014, Volume 205, Number 2, Pages 75–122 (Mi msb8251)  

This article is cited in 6 scientific papers (total in 6 papers)

A topological classification of the Chaplygin systems in the dynamics of a rigid body in a fluid

S. S. Nikolaenko

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: The paper is concerned with the topological analysis of the Chaplygin integrable case in the dynamics of a rigid body in a fluid. A full list of the topological types of Chaplygin systems in their dependence on the energy level is compiled on the basis of the Fomenko-Zieschang theory. An effective description of the topology of the Liouville foliation in terms of natural coordinate variables is also presented, which opens a direct way to calculating topological invariants. It turns out that on all nonsingular energy levels Chaplygin systems are Liouville equivalent to the well-known Euler case in the dynamics of a rigid body with fixed point.
Bibliography: 23 titles.

Keywords: Kirchhoff's equations, Chaplygin case, integrable Hamiltonian system, Liouville foliation, Fomenko-Zieschang invariant.

Funding Agency Grant Number
Russian Foundation for Basic Research 13-01-00664а
Ministry of Education and Science of the Russian Federation НШ-1410.2012.1
11.G34.31.0054


DOI: https://doi.org/10.4213/sm8251

Full text: PDF file (930 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2014, 205:2, 224–268

Bibliographic databases:

UDC: 517.938.5
MSC: Primary 37J35, 70E15; Secondary 70E40
Received: 04.06.2013

Citation: S. S. Nikolaenko, “A topological classification of the Chaplygin systems in the dynamics of a rigid body in a fluid”, Mat. Sb., 205:2 (2014), 75–122; Sb. Math., 205:2 (2014), 224–268

Citation in format AMSBIB
\Bibitem{Nik14}
\by S.~S.~Nikolaenko
\paper A topological classification of the Chaplygin systems in the dynamics of a~rigid body in a~fluid
\jour Mat. Sb.
\yr 2014
\vol 205
\issue 2
\pages 75--122
\mathnet{http://mi.mathnet.ru/msb8251}
\crossref{https://doi.org/10.4213/sm8251}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3204669}
\zmath{https://zbmath.org/?q=an:06351086}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2014SbMat.205..224N}
\elib{http://elibrary.ru/item.asp?id=21277066}
\transl
\jour Sb. Math.
\yr 2014
\vol 205
\issue 2
\pages 224--268
\crossref{https://doi.org/10.1070/SM2014v205n02ABEH004373}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000334592600003}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84898991152}


Linking options:
  • http://mi.mathnet.ru/eng/msb8251
  • https://doi.org/10.4213/sm8251
  • http://mi.mathnet.ru/eng/msb/v205/i2/p75

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. A. T. Fomenko, S. S. Nikolaenko, “The Chaplygin case in dynamics of a rigid body in fluid is orbitally equivalent to the Euler case in rigid body dynamics and to the Jacobi problem about geodesics on the ellipsoid”, J. Geom. Phys., 87 (2015), 115–133  crossref  mathscinet  zmath  isi  elib  scopus
    2. M. P. Kharlamov, H. M. Yehia, “Separation of variables in one case of motion of a gyrostat acted upon by gravity and magnetic fields”, Egyptian Journal of Basic and Applied Sciences, 2:3 (2015), 236–242  crossref
    3. S. S. Nikolaenko, “Topological classification of the Goryachev integrable case in rigid body dynamics”, Sb. Math., 207:1 (2016), 113–139  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. V. V. Vedyushkina (Fokicheva), A. T. Fomenko, “Integrable topological billiards and equivalent dynamical systems”, Izv. Math., 81:4 (2017), 688–733  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    5. S. S. Nikolaenko, “Topological classification of the Goryachev integrable systems in the rigid body dynamics: non-compact case”, Lobachevskii J. Math., 38:6 (2017), 1050–1060  crossref  mathscinet  zmath  isi  scopus
    6. V. V. Vedyushkina (Fokicheva), A. T. Fomenko, “Integrable geodesic flows on orientable two-dimensional surfaces and topological billiards”, Izv. Math., 83:6 (2019), 1137–1173  mathnet  crossref  crossref  adsnasa  isi  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
    Number of views:
    This page:332
    Full text:107
    References:64
    First page:46

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020