Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Parking 3-sphere swimmer. I. Energy minimizing strokes   The paper is about the parking 3-sphere swimmer ($\text{sPr}_3$). This is a
low-Reynolds number model swimmer composed of three balls of equal radii. The
three balls can move along three horizontal axes (supported in the same plane)
that mutually meet at the center of $\text{sPr}_3$ with angles of $120^{\circ}$
. The governing dynamical system is introduced and the implications of its
geometric symmetries revealed. It is then shown that, in the first order range
of small strokes, optimal periodic strokes are ellipses embedded in 3d space,
i.e. closed curves of the form $t\in [0,2\pi] \mapsto (\cos t)u + (\sin t)v$
for suitable orthogonal vectors $u$ and $v$ of $\mathbb{R}^3$. A simple
analytic expression for the vectors $u$ and $v$ is derived. The results of the
paper are used in a second article where the real physical dynamics of
$\text{sPr}_3$ is analyzed in the asymptotic range of very long arms.

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The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
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The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol