Аннотация:
This paper is concerned with the study of permanent rotations of a rigid body
rolling without slipping on a horizontal plane (i. e., the velocity of the point of contact of the
ellipsoid with the plane is zero). By permanent rotations we will mean motions of a rigid body on
a horizontal plane such that the angular velocity of the body remains constant and the point of
contact does not change its position. A more detailed analysis is made of permanent rotations of
an omnirotational ellipsoid whose characteristic feature is the possibility of permanent rotations
about any point of its surface.
The work of I. A. Bizyaev (Sections 2, 4, 5 and 6) was supported by the Russian Science
Foundation (No. 21-71-10039). The work of I. S. Mamaev was carried out within the framework of
the state assignment of the Ministry of Science and Higher Education of Russia (FZZN-2020-0011).
Поступила в редакцию: 10.02.2022 Принята в печать: 04.05.2022
Образец цитирования:
Ivan A. Bizyaev, Ivan S. Mamaev, “Permanent Rotations in Nonholonomic Mechanics.
Omnirotational Ellipsoid”, Regul. Chaotic Dyn., 27:6 (2022), 587–612
\RBibitem{BizMam22}
\by Ivan A. Bizyaev, Ivan S. Mamaev
\paper Permanent Rotations in Nonholonomic Mechanics.
Omnirotational Ellipsoid
\jour Regul. Chaotic Dyn.
\yr 2022
\vol 27
\issue 6
\pages 587--612
\mathnet{http://mi.mathnet.ru/rcd1182}
\crossref{https://doi.org/10.1134/S1560354722060016}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4519668}
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd1182
https://www.mathnet.ru/rus/rcd/v27/i6/p587
Эта публикация цитируется в следующих 6 статьяx:
Maria Przybylska, Andrzej J. Maciejewski, “Top on a smooth plane”, Chaos: An Interdisciplinary Journal of Nonlinear Science, 34:4 (2024)
Alexander A. Kilin, Elena N. Pivovarova, “Bifurcation analysis of the problem of a “rubber” ellipsoid of revolution rolling on a plane”, Nonlinear Dyn, 2024
Alexander A. Kilin, Elena N. Pivovarova, “Dynamics of an Unbalanced Disk
with a Single Nonholonomic Constraint”, Regul. Chaotic Dyn., 28:1 (2023), 78–106
G. M. Rozenblat, “Peculiarities of Statics and Dynamics of the Heavy Ellipsoid on the Rough Inclined Plane”, Прикладная математика и механика, 87:4 (2023), 557
Alexander A. Kilin, Elena N. Pivovarova, “Stability of Vertical Rotations of an Axisymmetric Ellipsoid on a Vibrating Plane”, Mathematics, 11:18 (2023), 3948
G. M. Rozenblat, “Features of Statics and Dynamics of a Heavy Ellipsoid on a Rough Inclined Plane”, Mech. Solids, 58:7 (2023), 2504
Цитирование в формате AMSBIB
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