Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the energy partition in oscillations and waves   A class of generally nonlinear dynamical systems is considered, for which the
Lagrangian is represented as a sum of homogeneous functions of the
displacements and their derivatives. It is shown that an energy partition as a
single relation follows directly from the Euler-Lagrange equation in its
general form. It is defined solely by the homogeneity orders. If the potential
energy is represented by a single homogeneous function, as well as the kinetic
energy, the partition between these energies is defined uniquely. Finite
discrete systems, finite continual bodies, homogeneous and periodic-structure
waveguides are considered. The general results are illustrated by examples of
various types of oscillations and waves, linear and nonlinear, homogeneous and
forced, steady-state and transient, periodic, non-periodic and solitary,
regular, parametric and resonant. The reduced energy partition relation for
statics is also presented.

31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph