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Эта публикация цитируется в 3 научных статьях (всего в 3 статьях)
Alexey Borisov Memorial Volume
Spherical and Planar Ball Bearings — Nonholonomic Systems
with Invariant Measures
Vladimir Dragovićab, Borislav Gajića, Bozidar Jovanovića a Mathematical Institute, Serbian Academy of Sciences and Arts,
Kneza Mihaila 36, 11001 Belgrade, Serbia
b Department of Mathematical Sciences, The University of Texas at Dallas,
800 West Campbell Road, 75080 Richardson TX, USA
Аннотация:
We first construct nonholonomic systems of $n$ homogeneous balls $\mathbf B_1,\dots,\mathbf B_n$ with centers $O_1,\ldots,O_n$ and with the same radius $r$ that are rolling without slipping around a fixed sphere $\mathbf S_0$ with center $O$ and radius $R$. In addition, it is assumed that a dynamically nonsymmetric sphere $\mathbf S$ of radius $R+2r$ and the center that coincides with the center $O$ of the fixed sphere $\mathbf S_0$ rolls without slipping over the moving balls $\mathbf B_1,\dots,\mathbf B_n$.
We prove that these systems possess an invariant measure. As the second task, we consider the limit, when the radius $R$ tends to infinity. We obtain a corresponding planar problem consisting of $n$ homogeneous balls $\mathbf B_1,\dots,\mathbf B_n$ with centers $O_1,\ldots,O_n$ and the same radius $r$ that are rolling without slipping
over a fixed plane $\Sigma_0$, and a moving plane $\Sigma$ that moves without slipping over the homogeneous balls. We prove that this system possesses an invariant measure and that it is integrable in quadratures according to the Euler – Jacobi theorem.
Ключевые слова:
nonholonimic dynamics, rolling without slipping, invariant measure, integrability.
Поступила в редакцию: 02.11.2022 Принята в печать: 02.05.2022
Образец цитирования:
Vladimir Dragović, Borislav Gajić, Bozidar Jovanović, “Spherical and Planar Ball Bearings — Nonholonomic Systems
with Invariant Measures”, Regul. Chaotic Dyn., 27:4 (2022), 424–442
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd1173 https://www.mathnet.ru/rus/rcd/v27/i4/p424
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