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

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.


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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
\by I.~A.~Bizyaev, A.~V.~Borisov, I.~S.~Mamaev
\paper The Hess--Appelrot system and its nonholonomic analogs
\inbook Modern problems of mathematics, mechanics, and mathematical physics.~II
\bookinfo Collected papers
\serial Trudy Mat. Inst. Steklova
\yr 2016
\vol 294
\pages 268--292
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\jour Proc. Steklov Inst. Math.
\yr 2016
\vol 294
\pages 252--275

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    This publication is cited in the following articles:
    1. 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
    2. 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
    3. I. A. Bizyaev, A. V. Borisov, I. S. Mamaev, “Sluchai Gessa–Appelrota i kvantovanie chisla vrascheniya”, Nelineinaya dinam., 13:3 (2017), 433–452  mathnet  crossref  mathscinet  elib
    4. 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  crossref  mathscinet  zmath  isi  scopus
    5. A. Borisov, I. Mamaev, “Rigid body dynamics”, Rigid Body Dynamics, de Gruyter Studies in Mathematical Physics, 52, Walter de Gruyter Gmbh, 2019, 1–520  mathscinet  isi
    6. 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  mathnet  crossref
    7. 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  mathnet  crossref  elib
    8. 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  crossref  isi
    9. 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  mathnet  crossref
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