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Mat. Sb., 2008, Volume 199, Number 6, Pages 85–104 (Mi msb3971)  

This article is cited in 8 scientific papers (total in 8 papers)

Topological analysis of the motion of an ellipsoid on a smooth plane

M. Yu. Ivochkin

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

Abstract: The problem of the motion of a dynamically and geometrically symmetric heavy ellipsoid on a smooth horizontal plane is investigated. The problem is integrable and can be considered a generalization of the problem of motion of a heavy rigid body with fixed point in the Lagrangian case. The Smale bifurcation diagrams are constructed. Surgeries of tori are investigated using methods developed by Fomenko and his students.
Bibliography: 9 titles.

DOI: https://doi.org/10.4213/sm3971

Full text: PDF file (743 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2008, 199:6, 871–890

Bibliographic databases:

UDC: 514.853
MSC: 37J35, 70H06
Received: 01.11.2007

Citation: M. Yu. Ivochkin, “Topological analysis of the motion of an ellipsoid on a smooth plane”, Mat. Sb., 199:6 (2008), 85–104; Sb. Math., 199:6 (2008), 871–890

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. A. V. Bolsinov, A. V. Borisov, I. S. Mamaev, “Topology and stability of integrable systems”, Russian Math. Surveys, 65:2 (2010), 259–318  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. A. V. Bolsinov, A. A. Kilin, A. O. Kazakov, “Topologicheskaya monodromiya v negolonomnykh sistemakh”, Nelineinaya dinam., 9:2 (2013), 203–227  mathnet
    3. P. A. Elkin, “Poincaré–Chetaev bifurcation diagrams in the problem of motion of an inhomogeneous dynamically and geometrically symmetric ellipsoid on a smooth plane”, Moscow University Mechanics Bulletin, 68:4 (2013), 106–109  mathnet  crossref
    4. G. E. Smirnov, “Fokusnye osobennosti v klassicheskoi mekhanike”, Nelineinaya dinam., 10:1 (2014), 101–112  mathnet
    5. A.V. Bolsinov, A.A. Kilin, A.O. Kazakov, “Topological monodromy as an obstruction to Hamiltonization of nonholonomic systems: Pro or contra?”, Journal of Geometry and Physics, 2014  crossref  mathscinet  scopus
    6. E. O. Kantonistova, “Topological classification of integrable Hamiltonian systems in a potential field on surfaces of revolution”, Sb. Math., 207:3 (2016), 358–399  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    7. Dullin H.R., Pelayo A., “Generating Hyperbolic Singularities in Semitoric Systems Via Hopf Bifurcations”, J. Nonlinear Sci., 26:3 (2016), 787–811  crossref  mathscinet  zmath  isi  scopus
    8. Kozlov I., Oshemkov A., “Integrable Systems With Linear Periodic Integral For the Lie Algebra E(3)”, Lobachevskii J. Math., 38:6 (2017), 1014–1026  crossref  mathscinet  zmath  isi  scopus
  • Математический сборник Sbornik: Mathematics (from 1967)
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