Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Annihilation of Relative Equilibria in the Gravitational Field of
  Irregular-shaped Minor Celestial Bodies   The rotational speeds of irregular shaped minor celestial bodies can be
changed by the YORP effect. This variation in speed can make the numbers,
positions, stabilities, and topological cases of the minor body s relative
equilibrium points vary. The numbers of relative equilibrium points can be
reduced through the collision and annihilation of relative equilibrium points,
or increase through the creation and separation of relative equilibrium points.
Here we develop a classification system of multiple annihilation behaviors of
the equilibrium points for irregular shaped minor celestial bodies. Most minor
bodies have five equilibrium points; there are twice the number of
annihilations per equilibrium point when the number of equilibrium points is
between one and five. We present the detailed annihilation classifications for
equilibria of objects which have five equilibrium points. Additionally, the
annihilation classification for the seven equilibria of Kleopatra shaped
objects and the nine equilibria of Bennu shaped objects are also discussed.
Equilibria of different objects fall into different annihilation
classifications. By letting the rotational speeds vary, we studied the
annihilations and creations of relative equilibria in the gravitational field
of ten minor bodies.

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The categories of this paper are: patt-sol
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The categories of this paper are: hep-lat
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The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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The categories of this paper are: cs
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The categories of this paper are: q-bio
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The categories of this paper are: math
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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: hep-th
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The categories of this paper are: math-ph
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The categories of this paper are: q-fin
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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: eess
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The categories of this paper are: cond-mat