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- W4320855584 abstract "We consider the nonholonomic systems of $n$ homogeneous balls $mathbf B_1,dots,mathbf B_n$ with the same radius $r$ that are rolling without slipping about a fixed sphere $mathbf S_0$ with center $O$ and radius $R$. In addition, it is assumed that a dynamically nonsymmetric sphere $mathbf S$ with the center that coincides with the center $O$ of the fixed sphere $mathbf S_0$ rolls without slipping in contact to the moving balls $mathbf B_1,dots,mathbf B_n$. The problem is considered in four different configurations. We derive the equations of motion and prove that these systems possess an invariant measure. As the main result, for $n=1$ we found two cases that are integrable in quadratures according to the Euler-Jacobi theorem. The obtained integrable nonholonomic models are natural extensions of the well-known Chaplygin ball integrable problems. Further, we explicitly integrate the planar problem consisting of $n$ homogeneous balls of the same radius, but with different masses, that roll without slipping over a fixed plane $Sigma_0$ with a plane $Sigma$ that moves without slipping over these balls." @default.
- W4320855584 created "2023-02-16" @default.
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- W4320855584 date "2022-10-20" @default.
- W4320855584 modified "2023-09-23" @default.
- W4320855584 title "Spherical and Planar Ball Bearings -- a Study of Integrable Cases" @default.
- W4320855584 doi "https://doi.org/10.48550/arxiv.2210.11586" @default.
- W4320855584 hasPublicationYear "2022" @default.
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