Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An exact Lagrangian integral for the Newtonian gravitational field
  strength   An exact expression for the gravitational field strength in a
self-gravitating dust continuum is derived within the Lagrangian picture of
continuum mechanics. From the Euler-Newton system a transport equation for the
gravitational field strength is formulated and then integrated along
trajectories of continuum elements. The resulting integral solves one of the
Lagrangian equations of the corresponding Lagrange-Newton system in general.
Relations to known exact solutions without symmetry in Newtonian gravity are
discussed. The presented integral may be employed to access the
non-perturbative regime of structure formation in Newtonian cosmology, and to
apply iterative Lagrangian schemes to solve the Lagrange-Newton system.

1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat