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Trudy Mat. Inst. Steklova, 2016, Volume 294, Pages 268–292
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This article is cited in 9 scientific papers (total in 9 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:
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English version:
Proceedings of the Steklov Institute of Mathematics, 2016, 294, 252–275
Bibliographic databases:
   
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, Trudy Mat. Inst. Steklova, 294, MAIK Nauka/Interperiodica, Moscow, 2016, 268–292; Proc. Steklov Inst. Math., 294 (2016), 252–275
Citation in format AMSBIB
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Linking options:
http://mi.mathnet.ru/eng/tm3726https://doi.org/10.1134/S0371968516030171 http://mi.mathnet.ru/eng/tm/v294/p268
Citing articles on Google Scholar:
Russian citations,
English citations
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This publication is cited in the following articles:
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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
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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
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I. A. Bizyaev, A. V. Borisov, I. S. Mamaev, “Sluchai Gessa–Appelrota i kvantovanie chisla vrascheniya”, Nelineinaya dinam., 13:3 (2017), 433–452
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A. Borisov, A. Kilin, I. Mamaev, “Invariant submanifolds of genus 5 and a cantor staircase in the nonholonomic model of a snakeboard”, Int. J. Bifurcation Chaos, 29:3 (2019), 1930008
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A. Borisov, I. Mamaev, “Rigid body dynamics”, Rigid Body Dynamics, de Gruyter Studies in Mathematical Physics, 52, Walter de Gruyter Gmbh, 2019, 1–520
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Alexander A. Burov, Anna D. Guerman, Vasily I. Nikonov, “Asymptotic Invariant Surfaces for Non-Autonomous Pendulum-Type Systems”, Regul. Chaotic Dyn., 25:1 (2020), 121–130
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O. V. Kholostova, “On the Dynamics of a Rigid Body in the Hess Case at High-Frequency Vibrations of a Suspension Point”, Rus. J. Nonlin. Dyn., 16:1 (2020), 59–84
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A. A. Burov, “Linear invariant relations in the problem of the motion of a bundle of two bodies”, Dokl. Phys., 65:4 (2020), 147–148
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A. A. Kosov, E. I. Semenov, “O tochnykh resheniyakh uravnenii vraschatelnogo dvizheniya tverdogo tela pri deistvii momenta tsirkulyarno-giroskopicheskikh sil”, Zhurnal SVMO, 23:2 (2021), 159–170
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