Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the action principle for a system of differential equations   We consider the problem of constructing an action functional for physical
systems whose classical equations of motion cannot be directly identified with
Euler-Lagrange equations for an action principle. Two ways of action principle
construction are presented. From simple consideration, we derive necessary and
sufficient conditions for the existence of a multiplier matrix which can endow
a prescribed set of second-order differential equations with the structure of
Euler-Lagrange equations. An explicit form of the action is constructed in case
if such a multiplier exists. If a given set of differential equations cannot be
derived from an action principle, one can reformulate such a set in an
equivalent first-order form which can always be treated as the Euler-Lagrange
equations of a certain action. We construct such an action explicitly. There
exists an ambiguity (not reduced to a total time derivative) in associating a
Lagrange function with a given set of equations. We present a complete
description of this ambiguity. The general procedure is illustrated by several
examples.

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The categories of this paper are: cs
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
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The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
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The categories of this paper are: supr-con
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The categories of this paper are: mtrl-th
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: patt-sol
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The categories of this paper are: stat