Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A simple model for the location of Saturn's F ring   In this paper, we introduce a simplified model to understand the location of
Saturn's F ring. The model is a planar restricted five-body problem defined by
the gravitational field of Saturn, including its second zonal harmonic $J_2$,
the shepherd moons Prometheus and Pandora, and Titan. We compute accurate
long-time numerical integrations of (about 2.5 million) non-interacting
test-particles initially located in the region between the orbits of Prometheus
and Pandora, and address whether they escape or remain trapped in this region.
We obtain a wide region of initial conditions of the test particles that remain
confined. We consider a dynamical stability indicator for the test particles'
motion defined by computing the ratio of the standard deviation over the
average value of relevant dynamical quantities, in particular, for the
mean-motion and the semi-major axis. This indicator separates clearly a subset
of trapped initial conditions that appear as very localized stripes in the
initial semi-major axis and eccentricity space for the most stable orbits.
Retaining only these test particles, we obtain a narrow eccentric ring which
displays sharp edges and collective alignment. The semi-major axis of the
accumulation stripes of the stable ring-particles can be associated with
resonances, mostly involving Prometheus' outer Lindblad and co-rotation
resonances, but not exclusively. Pandora's inner Lindblad and co-rotation
resonances as well as low-order three-body resonances typically coincide with
gaps, i.e., regions of instabilities. Comparison of our results with the
nominal data for the F ring shows some correspondence.

22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs