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.
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
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\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
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\jour Proc. Steklov Inst. Math.
\yr 2016
\vol 294
\pages 252--275
\crossref{https://doi.org/10.1134/S0081543816060171}
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Linking options:
https://www.mathnet.ru/eng/tm3726
https://doi.org/10.1134/S0371968516030171
https://www.mathnet.ru/eng/tm/v294/p268
This publication is cited in the following 11 articles:
A. A. Kosov, “On Analogues of the Hess Case for a Gyrostat under the Action of the Moment of Gyroscopic and Circular Forces”, Mech. Solids, 57:8 (2022), 1848
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
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
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
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
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
A. Borisov, I. Mamaev, “Rigid body dynamics”, Rigid Body Dynamics, de Gruyter Studies in Mathematical Physics, 52, Walter de Gruyter Gmbh, 2019, 1–520
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
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
I. A. Bizyaev, A. V. Borisov, I. S. Mamaev, “Sluchai Gessa–Appelrota i kvantovanie chisla vrascheniya”, Nelineinaya dinam., 13:3 (2017), 433–452
Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev, “The Hess–Appelrot case and quantization of the rotation number”, Regul. Chaot. Dyn., 22:2 (2017), 180
Citation in format AMSBIB
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