Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the circular Sitnikov problem: the alternation of stability and
  instability in the family of vertical motions   We consider the special case of the restricted circular three-body problem,
when the two primaries are of equal mass, while the third body of negligible
mass performs oscillations along a straight line perpendicular to the plane of
the primaries (so called periodic vertical motions). The main goal of our
investigation is to study the stability of these periodic motions in the linear
approximation. A special attention is given to the alternation of stability and
instability within the family of periodic vertical motions, whenever their
amplitude is varied in a continuous monotone manner.

5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con