Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Euler configurations and quasi-polynomial systems   In the Newtonian 3-body problem, for any choice of the three masses, there
are exactly three Euler configurations (also known as the three Euler points).
In Helmholtz' problem of 3 point vortices in the plane, there are at most three
collinear relative equilibria. The "at most three" part is common to both
statements, but the respective arguments for it are usually so different that
one could think of a casual coincidence. By proving a statement on a
quasi-polynomial system, we show that the "at most three" holds in a general
context which includes both cases. We indicate some hard conjectures about the
configurations of relative equilibrium and suggest they could be attacked
within the quasi-polynomial framework.

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The categories of this paper are: supr-con
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The categories of this paper are: nucl-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: cs
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The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: chem-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys
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The categories of this paper are: nlin
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The categories of this paper are: patt-sol
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The categories of this paper are: eess
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The categories of this paper are: econ
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The categories of this paper are: hep-ex
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The categories of this paper are: funct-an