Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Closed, spirograph-like orbits in power law central potentials   Bertrand's theorem proves that inverse square and Hooke's law-type central
forces are the only ones for which all bounded orbits are closed. Similar
analysis was used to show that for other central force laws there exist closed
orbits for a discrete set of angular momentum and energy values. These orbits
can in general be characterized as ``spirograph''-like, although specific
orbits look more ``star''-like or ``triangular.'' We use the results of a
perturbative version of Bertrand's theorem to predict which values of angular
momentum and energy result in closed orbits, and what their shapes will be.

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The categories of this paper are: hep-ph
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga