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Mat. Sb., 2014, Volume 205, Number 7, Pages 115–134 (Mi msb8297)  

This article is cited in 3 scientific papers (total in 3 papers)

The phase topology of a special case of Goryachev integrability in rigid body dynamics

P. E. Ryabov

Financial University under the Government of the Russian Federation, Moscow

Abstract: The phase topology of a special case of Goryachev integrability in the problem of motion of a rigid body in a fluid is investigated using the method of Boolean functions, which was developed by Kharlamov for algebraically separated systems. The bifurcation diagram of the moment map is found and the Fomenko invariant, which classifies the systems up to rough Liouville equivalence, is specified.
Bibliography: 15 titles.

Keywords: Kirchhoff's equations, completely integrable Hamiltonian systems, algebraic separation of variables, bifurcation diagram, bifurcations of Liouville tori.

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-00119
Government of the Volgograd region 13-01-97025


DOI: https://doi.org/10.4213/sm8297

Full text: PDF file (660 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2014, 205:7, 1024–1044

Bibliographic databases:

UDC: 514.853+517.938.5
MSC: 37J35, 37N10
Received: 06.11.2013

Citation: P. E. Ryabov, “The phase topology of a special case of Goryachev integrability in rigid body dynamics”, Mat. Sb., 205:7 (2014), 115–134; Sb. Math., 205:7 (2014), 1024–1044

Citation in format AMSBIB
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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. 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
    2. 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
    3. 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
  • Математический сборник Sbornik: Mathematics (from 1967)
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