Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Notes on relative equilibria of isosceles molecules in classical
  approximation   We study a classical model of isosceles triatomic "A-B-A" molecules. The
atoms, considered mass points, interact mutually via a generic
repulsive-attractive binary potential.
  First we show that the steady states, or relative equilibria (RE),
corresponding to rotations about the molecule symmetry axis may be determined
qualitatively assuming the knowledge of 1) the shape of the binary interaction
potential, 2) the equilibrium diatomic distances (i.e., the equilibrium bond
length) of the A-A and A-B molecules, and 3) the distance at which the RE of
the diatomic A-A molecule ceases to exist. No analytic expression for the
interaction potentials is needed.
  Second we determine the stability of the isosceles RE modulo rotations using
geometric mechanics methods and using Lennard-Jones diatomic potentials. As a
by-product, we verify the qualitative results on RE existence and bifurcation.
For isosceles RE we employ the Reduced Energy-Momentum method presented in
[J.E. Marsden, Lectures in Mechanics, Cambridge University Press, 1992],
whereas for linear (trivial isosceles) RE we apply the Symplectic Slice method,
a technique based on the findings in the paper [R.M. Roberts, T. Schmah and C.
Stoica, Relative equilibria for systems with configurations space isotropy, J.
Geom. Phys., 56, 762, (2006)].

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The categories of this paper are: hep-lat
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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: quant-ph
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The categories of this paper are: funct-an
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The categories of this paper are: supr-con
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The categories of this paper are: chem-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: q-bio
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The categories of this paper are: cond-mat
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The categories of this paper are: bayes-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: econ
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ph