This paper is concerned with the motion of an unbalanced dynamically symmetric sphere rolling without slipping on a plane in the presence of an external magnetic field. It is assumed that the sphere can consist completely or partially of dielectric, ferromagnetic, superconducting and crystalline materials. According to the existing phenomenological theory, the analysis of the sphere’s dynamics requires in this case taking into account the Lorentz torque, the Barnett-London effect and the Einstein-de Haas effect. Using this mathematical model, we have obtained conditions for the existence of integrals of motion which allow one to reduce integration of the equations of motion to a quadrature similar to the Lagrange quadrature for a heavy rigid body.

中文翻译：

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关于磁场中的非完整劳斯球

本文关注的是不对称动态对称球体滚动的运动，该运动在存在外部磁场的情况下不会在平面上滑动。假定该球体可以全部或部分由介电，铁磁，超导和晶体材料组成。根据现有的现象学理论，在这种情况下，要对球体的动力学进行分析，需要考虑洛伦兹转矩，巴内特-伦敦效应和爱因斯坦-德哈斯效应。使用这一数学模型，我们获得了运动积分存在的条件，该条件使人们可以将运动方程的积分减小到与重型刚体的拉格朗日正交相似的正交。