Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The rigid body dynamics: classical and algebro-geometric integration   The basic notion for a motion of a heavy rigid body fixed at a point in
three-dimensional space as well as its higher-dimensional generalizations are
presented. On a basis of Lax representation, the algebro-geometric integration
procedure for one of the classical cases of motion of three-dimensional rigid
body - the Hess-Appel'rot system is given. The classical integration in Hess
coordinates is presented also. For higher-dimensional generalizations, the
special attention is paid in dimension four. The L-A pairs and the classical
integration procedures for completely integrable four-dimensional rigid body so
called the Lagrange bitop as well as for four-dimensional generalization of
Hess-Appel'rot system are given. An $n$-dimensional generalization of the
Hess-Appel'rot system is also presented and its Lax representation is given.
Starting from another Lax representation for the Hess-Appel'rot system, a
family of dynamical systems on $e(3)$ is constructed. For five cases from the
family, the classical and algebro-geometric integration procedures are
presented. The four-dimensional generalizations for the Kirchhoff and the
Chaplygin cases of motion of rigid body in ideal fluid are defined. The results
presented in the paper are part of results obtained in last decade.

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The categories of this paper are: mtrl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: supr-con
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The categories of this paper are: solv-int
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The categories of this paper are: ao-sci
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The categories of this paper are: cmp-lg
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The categories of this paper are: econ
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
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The categories of this paper are: alg-geom
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The categories of this paper are: quant-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-lat