Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Inverse Variational Problem and Symmetry in Action: The Relativistic
  Third Order Dynamics   Tools of the intrinsic analysis on manifolds, helpful in solving the
invariant inverse problem of the calculus of variations are being presented
comprising a combined approach which consists in the simultaneous imposition of
symmetry principles and the inverse variational problem considerations in terms
of vector-valued differential forms. In three-dimensional space-time we obtain
a unique (covector) third-order Poincar\'e-invariant variational equation,
which then is identified with the motion of a free relativistic top in flat
three-dimensional space-time.

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The categories of this paper are: plasm-ph
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The categories of this paper are: eess
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
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The categories of this paper are: chem-ph
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The categories of this paper are: q-alg
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The categories of this paper are: funct-an
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The categories of this paper are: atom-ph
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The categories of this paper are: solv-int
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The categories of this paper are: hep-lat
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The categories of this paper are: alg-geom
1
The categories of this paper are: cs
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The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci