Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Intrinsic Equations For a Relaxed Elastic Line of Second Kind on an
  Oriented Surface   Let {\alpha}(s) be an arc on a connected oriented surface S in E3,
parameterized by arc length s, with torsion {\tau} and length l. The total
square torsion F of {\alpha} is defined by T=\int_{0}^{l}\tau ^{2}ds\ $. . The
arc {\alpha} is called a relaxed elastic line of second kind if it is an
extremal for the variational problem of minimizing the value of F within the
family of all arcs of length l on S having the same initial point and initial
direction as {\alpha}. In this study, we obtain differential equation and
boundary conditions for a relaxed elastic line of second kind on an oriented
surface.

21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph