Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: General solution of the Jeans equations for triaxial galaxies with
  separable potentials   The Jeans equations relate the second-order velocity moments to the density
and potential of a stellar system. For general three-dimensional stellar
systems, there are three equations and six independent moments. By assuming
that the potential is triaxial and of separable Staeckel form, the mixed
moments vanish in confocal ellipsoidal coordinates. Consequently, the three
Jeans equations and three remaining non-vanishing moments form a closed system
of three highly-symmetric coupled first-order partial differential equations in
three variables. These equations were first derived by Lynden-Bell, over 40
years ago, but have resisted solution by standard methods. We present the
general solution here.
  We consider the two-dimensional limiting cases first. We solve their Jeans
equations by a new method which superposes singular solutions. The singular
solutions, which are new, are standard Riemann-Green functions. The
two-dimensional solutions are applied to non-axisymmetric discs, oblate and
prolate spheroids, and also to the scale-free triaxial limit. We then extend
the method of singular solutions to the triaxial case, and obtain a full
solution. The general solution can be expressed in terms of complete
(hyper)elliptic integrals which can be evaluated in a straightforward way, and
provides the full set of second moments which can support a triaxial density
distribution in a separable triaxial potential. (abridged)

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The categories of this paper are: plasm-ph
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The categories of this paper are: stat
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The categories of this paper are: cmp-lg
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The categories of this paper are: eess
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The categories of this paper are: acc-phys
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The categories of this paper are: alg-geom
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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: quant-ph
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The categories of this paper are: econ
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The categories of this paper are: physics
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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: supr-con
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The categories of this paper are: funct-an
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The categories of this paper are: cond-mat