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Tr. Mat. Inst. Steklova, 2016, Volume 294, Pages 268–292 (Mi tm3726)  

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

The Hess–Appelrot system and its nonholonomic analogs

I. A. Bizyaev, A. V. Borisov, I. S. Mamaev

Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia

Abstract: This paper is concerned with the nonholonomic Suslov problem and its generalization proposed by Chaplygin. The issue of the existence of an invariant measure with singular density (having singularities at some points of the phase space) is discussed.

Funding Agency Grant Number
Russian Science Foundation 14-50-00005
This work is supported by the Russian Science Foundation under grant 14-50-00005.


DOI: https://doi.org/10.1134/S0371968516030171

Full text: PDF file (993 kB)
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English version:
Proceedings of the Steklov Institute of Mathematics, 2016, 294, 252–275

Bibliographic databases:

Document Type: Article
UDC: 517.925+531.381
Received: April 25, 2016

Citation: I. A. Bizyaev, A. V. Borisov, I. S. Mamaev, “The Hess–Appelrot system and its nonholonomic analogs”, Modern problems of mathematics, mechanics, and mathematical physics. II, Collected papers, Tr. Mat. Inst. Steklova, 294, MAIK Nauka/Interperiodica, Moscow, 2016, 268–292; Proc. Steklov Inst. Math., 294 (2016), 252–275

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  • https://doi.org/10.1134/S0371968516030171
  • http://mi.mathnet.ru/eng/tm/v294/p268

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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. Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev, “The Hess–Appelrot Case and Quantization of the Rotation Number”, Regul. Chaotic Dyn., 22:2 (2017), 180–196  mathnet  crossref  mathscinet  zmath
    2. A. V. Borisov, I. S. Mamaev, I. A. Bizyaev, “Dynamical systems with non-integrable constraints, vakonomic mechanics, sub-Riemannian geometry, and non-holonomic mechanics”, Russian Math. Surveys, 72:5 (2017), 783–840  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    3. Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev, “The Chaplygin Sleigh with Parametric Excitation: Chaotic Dynamics and Nonholonomic Acceleration”, Regul. Chaotic Dyn., 22:8 (2017), 955–975  mathnet  crossref
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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