We consider the possibility of using Dirac’s ideas of the deformation of Poisson brackets in nonholonomic mechanics. As an example, we analyze the composition of external forces that do no work and reaction forces of nonintegrable constraints in the model of a nonholonomic Chaplygin sphere on a plane. We prove that, when a solenoidal field is applied, the general mechanical energy, the invariant measure and the conformally Hamiltonian representation of the equations of motion are preserved. In addition, we consider the case of motion of the nonholonomic Chaplygin sphere in a constant magnetic field taking dielectric and ferromagnetic (superconducting) properties of the sphere into account. As a by-product we also obtain two new integrable cases of the Hamiltonian rigid body dynamics in a constant magnetic field taking the magnetization by rotation effect into account.

中文翻译：

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在磁场中的Chaplygin球上

我们考虑在非完整力学中使用狄拉克关于泊松托架变形的思想的可能性。例如，我们在平面上的非完整Chaplygin球面模型中分析了不起作用的外力的组成以及不可积分约束的反作用力。我们证明，当施加螺线管磁场时，运动方程的一般机械能，不变量度和保形哈密顿量表示得以保留。此外，我们考虑了非完整的Chaplygin球在恒定磁场中的运动情况，并考虑了该球的介电和铁磁（超导）特性。