Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spherically restricted motion of a charge in the field of a magnetic
  dipole   We study the restricted motion of an electric charge in a spherical surface
in the field of a magnetic dipole. This is the classical non-relativistic
St\"oermer problem within a sphere, with the dipole in its centre. We start
from a Lagrangian approach which allows us to analyze the dynamical properties
of the system, such as the role of a velocity dependent potential, the
symmetries and the conservation properties. We derive the Hamilton equations of
motion and observe that in this restricted case the equations can be reduced to
a quadrature. From the Hamiltonian function we find for the polar angle an
equivalent one-dimensional system of a particle in the presence of an effective
potential. This equivalent potential function, which is a double well
potential, allows us to get a clear description of this dynamical problem. We
are able to find closed horizontal trajectories, as well as their period.
Depending on initial conditions, we can find also some bands covered by
non-periodic trajectories, as well as the conditions for the presence of loops.
Then we obtain by means of numerical integration different plots of the
trajectories in three dimensional graphs in the sphere. This restricted case of
the Stoermer problem, which is formally integrable, is still a nonlinear
problem with a complex and interesting dynamics and we believe that it can
offer the student a better grasp of the subject than the general three
dimensional case.

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The categories of this paper are: q-bio
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The categories of this paper are: mtrl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-th
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ph
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The categories of this paper are: econ
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The categories of this paper are: funct-an
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The categories of this paper are: math-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int
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The categories of this paper are: adap-org