Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Periodic and falling-free motion of an inverted spherical pendulum with
  a moving pivot point   For the system of an inverted spherical pendulum with friction and a
periodically moving pivot point we prove the existence of at least one periodic
solution with the additional property of being falling-free. The last means
that the pendulum never becomes horizontal along the considered periodic
solution. Presented proof is an application of some recent results in the fixed
point theory.

19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas