Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The classical Kepler problem and geodesic motion on spaces of constant
  curvature   In this paper we clarify and generalise previous work by Moser and Belbruno
concerning the link between the motions in the classical Kepler problem and
geodesic motion on spaces of constant curvature. Both problems can be
formulated as Hamiltonian systems and the phase flow in each system is
characterised by the value of the corresponding Hamiltonian and one other
parameter (the mass parameter in the Kepler problem and the curvature parameter
in the geodesic motion problem). Using a canonical transformation the
Hamiltonian vector field for the geodesic motion problem is transformed into
one which is proportional to that for the Kepler problem. Within this framework
the energy of the Kepler problem is equal to (minus) the curvature parameter of
the constant curvature space and the mass parameter is given by the value of
the Hamiltonian for the geodesic motion problem. We work with the corresponding
family of evolution spaces and present a unified treatment which is valid for
all values of energy continuously. As a result, there is a correspondence
between the constants of motion for both systems and the Runge-Lenz vector in
the Kepler problem arises in a natural way from the isometries of a space of
constant curvature. In addition, the canonical nature of the transformation
guarantees that the Poisson bracket Lie algebra of constants of motion for the
classical Kepler problem is identical to that associated with geodesic motion
on spaces of constant curvature.

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The categories of this paper are: alg-geom
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The categories of this paper are: acc-phys
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The categories of this paper are: chem-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: econ
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex
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The categories of this paper are: eess
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The categories of this paper are: cond-mat
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The categories of this paper are: supr-con
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The categories of this paper are: dg-ga
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The categories of this paper are: adap-org
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The categories of this paper are: quant-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: mtrl-th