Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the relation of Thomas rotation and angular velocity of reference
  frames   In the extensive literature dealing with the relativistic phenomenon of
Thomas rotation several methods have been developed for calculating the Thomas
rotation angle of a gyroscope along a circular world line. One of the most
appealing concepts, introduced in \cite{rindler}, is to consider a rotating
reference frame co-moving with the gyroscope, and relate the precession of the
gyroscope to the angular velocity of the reference frame. A recent paper
\cite{herrera}, however, applies this principle to three different co-moving
rotating reference frames and arrives at three different Thomas rotation
angles. The reason for this apparent paradox is that the principle of
\cite{rindler} is used for a situation to which it does not apply. In this
paper we rigorously examine the theoretical background and limitations of
applicability of the principle of \cite{rindler}. Along the way we also
establish some general properties of {\it rotating reference frames}, which may
be of independent interest.

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The categories of this paper are: gr-qc
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The categories of this paper are: q-bio
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: funct-an
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The categories of this paper are: q-alg
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: astro-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: dg-ga
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The categories of this paper are: q-fin
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The categories of this paper are: physics
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-th