Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Attracting and repelling 2-body problems on a family of surfaces of
  constant curvature   We first provide a classification of the pure rotational motion of 2
particles on a sphere interacting via a repelling potential. This is achieved
by providing a simple geometric equivalence between repelling particles and
attracting particles, and relying on previous work on the similar
classification for attracting particles. The second theme of the paper is to
study the 2-body problem on a surface of constant curvature treating the
curvature as a parameter, and with particular interest in how families of
relative equilibria and their stability behave as the curvature passes through
zero and changes sign. We consider two cases: firstly one where the particles
are always attracting throughout the family, and secondly where they are
attracting for negative curvature and repelling for positive curvature,
interpolated by no interaction when the curvature vanishes. Our analysis
clarifies the role of curvature in the existence and stability of relative
equilibria.

23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn