Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Revisiting Noether's Theorem on constants of motion   In this paper we revisit Noether's theorem on the constants of motion for
Lagrangian mechanical systems in the ODE case, with some new perspectives on
both the theoretical and the applied side. We make full use of invariance up to
a divergence, or, as we call it here, Bessel-Hagen (BH) invariance. By
recognizing that the Bessel-Hagen (BH) function need not be a total time
derivative, we can easily deduce nonlocal constants of motion. We prove that we
can always trivialize either the time change or the BH-function, so that, in
particular, BH-invariance turns out not to be more general than Noether's
original invariance. We also propose a version of time change that simplifies
some key formulas. Applications include Lane-Emden equation, dissipative
systems, homogeneous potentials and superintegrable systems. Most notably, we
give two derivations of the Laplace-Runge-Lenz vector for Kepler's problem that
require space and time change only, without BH invariance, one with and one
without use of the Lagrange equation.

10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn