Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Collision of a Hard Ball with Singular Points of the Boundary   Recently were introduced physical billiards where a moving particle is a hard
sphere rather than a point as in standard mathematical billiards. It has been
shown that in the same billiard tables the physical billiards may have totally
different dynamics than mathematical billiards. This difference appears if the
boundary of a billiard table has visible singularities (internal corners if the
billiard table is two-dimensional), i.e. the particle may collide with these
singular points. Here, we consider the collision of a hard ball with a visible
singular point and demonstrate that the motion of the smooth ball after
collision with a visible singular point is indeed the one that was used in the
studies of physical billiards. So such collision is equivalent to the elastic
reflection of hard ball's center off a sphere with the center at the singular
point and the same radius as the radius of the moving particle.

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The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: nlin
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The categories of this paper are: math-ph
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The categories of this paper are: hep-th
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The categories of this paper are: acc-phys
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The categories of this paper are: mtrl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: ao-sci
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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: physics
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The categories of this paper are: bayes-an