Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Chaplygin sphere in a magnetic field   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.

28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
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The categories of this paper are: stat
1
The categories of this paper are: cs
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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: q-fin