Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An inverted pendulum with a moving pivot point: examples of topological
  approach   Two examples concerning an application of topology in the study of the
dynamics of an inverted plain mathematical pendulum with a pivot point moving
along a horizontal straight line are considered. The first example is an
application of the Wa{\.z}ewski principle to the problem of the existence of a
solution without falling in the case of a arbitrary prescribed law of motion of
the pivot point. The second example is a proof of the existence of periodic
solution in the same system when the law of motion is periodic as well.
Moreover, in the second case it is also shown that along the obtained periodic
solution the pendulum never becomes horizontal (falls). The proof is an example
of application of the recent developments in the fixed point theory based on
the Lefschetz-Hopf theory.

12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int