Abstract

In this paper, we consider the motion of a nonholonomic Chaplygin sphere on a plane in a constant magnetic field under the assumption that the sphere has dielectric and ferromagnetic properties. We also obtain a generalization of the integrable case thanks to V.V. Kozlov in the problem of the motion of a symmetric rigid body about a fixed point in a constant magnetic field and present a new particular integrable case of such motion.

中文翻译：

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非完整的Chaplygin球在磁场中的运动，Grioli问题和Barnett-London效应

摘要

在本文中，我们假设非完整的Chaplygin球在恒定磁场中在平面上的运动，前提是该球具有介电和铁磁特性。由于在恒定磁场中对称刚体绕固定点运动的问题，我们还通过VV Kozlov对可积情况进行了概括，并提出了这种运动的新的特殊可积情况。