Spherical and Planar Ball Bearings — Nonholonomic Systems with Invariant Measures

نویسندگان

چکیده

We first construct nonholonomic systems of $n$ homogeneous balls $\mathbf B_1,\dots,\mathbf B_n$ with centers $O_1,...,O_n$ and the same radius $r$ that are rolling without slipping around a fixed sphere S_0$ center $O$ $R$. In addition, it is assumed dynamically nonsymmetric S$ $R+2r$ coincides rolls over moving B_n$. prove these possess an invariant measure. As second task, we consider limit, when $R$ tends to infinity. obtain corresponding planar problem consisting plane $\Sigma_0$, $\Sigma$ moves balls. this system possesses measure integrable in quadratures according Euler-Jacobi theorem.

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ژورنال

عنوان ژورنال: Regular & Chaotic Dynamics

سال: 2022

ISSN: ['1468-4845', '1560-3547']

DOI: https://doi.org/10.1134/s1560354722040037