Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Second Euler-Lagrange Equation of Variational Calculus on Time
  Scales   The fundamental problem of the calculus of variations on time scales concerns
the minimization of a delta-integral over all trajectories satisfying given
boundary conditions. In this paper we prove the second Euler-Lagrange necessary
optimality condition for optimal trajectories of variational problems on time
scales. As an example of application of the main result, we give an alternative
and simpler proof to the Noether theorem on time scales recently obtained in
[J. Math. Anal. Appl. 342 (2008), no. 2, 1220-1226].

12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat