Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the nonlinear dynamics of a position-dependent mass-driven
  Duffing-type oscillator: Lagrange and Newton equations' equivalence   Using a generalized coordinate along with a proper invertible coordinate
transformation, we show that the Euler-Lagrange equation used by Bagchi et al.
16 is in clear violation of the Hamilton's principle. We also show that
Newton's equation of motion they have used is not in a form that satisfies the
dynamics of position-dependent mass (PDM) settings.. The equivalence between
Euler-Lagrange's and Newton's equations is now proved and documented through
the proper invertible coordinate transformation and the introduction of a new
PDM byproducted reaction-type force. The total mechanical energy for the PDM is
shown to be conservative (i.e., dE/dt=0, unlike Bagchi et al.'s 16
observation).

22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph