Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mechanical Snell's Law   We investigate the motion of a massive particle constrained to move along a
path consisting of two line segments on a vertical plane under an arbitrary
conservative force. By fixing the starting and end points of the track and
varying the vertex horizontally, we find the least-time path. We define the
angles of incidence and refraction similar to the refraction of a light ray. It
is remarkable that the ratio of the sines of these angles is identical to the
ratio of the average speeds on the two partial paths as long as the horizontal
component of the conservative force vanishes.

11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
2
The categories of this paper are: math
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas