# On the Chaplygin Sphere in a Magnetic Field

*2019, Volume 24, Number 6, pp. 739-754*

Author(s):

**Borisov A. V., Tsiganov A. V.**

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.

Access to the full text on the Springer website |