Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Conjugated equilibrium solutions for the $2$--body problem in the two
  dimensional sphere $\mathbb{M}^2_R$ for equal masses   We study here the behaviour of solutions for conjugated (antipodal) points in
the $2$-body problem on the two-dimensional sphere $\mathbb{M}^2_R$. We use a
slight modification of the classical potential used commonly in \cite{Borisov},
\cite{Diacu} and \cite{Perez}, which avoids the conjugated (antipodal) points
as singularities and permit us obtain solutions through these points, as limit
of relative equilibria. Such limit solutions behave as relative equilibria
because are invariant under Killing vector fields in the Lie Algebra ${\rm su}
(2)$ and are geodesic curves.

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The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
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The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
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The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: eess
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The categories of this paper are: adap-org