Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Kinematic Image of RR, PR, and RP Dyads   We provide necessary and sufficient conditions for admissible transformations
in the projectivised dual quaternion model of rigid body displacements and we
characterise constraint varieties of dyads with revolute and prismatic joints
in this model. Projective transformations induced by coordinate changes in
moving and/or fixed frame fix the quadrics of a pencil and preserve the two
families of rulings of an exceptional three-dimensional quadric. The constraint
variety of a dyad with two revolute joints is a regular ruled quadric in a
three-space that contains a "null quadrilateral". If a revolute joint is
replaced by a prismatic joint, this quadrilateral collapses into a pair of
conjugate complex null lines and a real line but these properties are not
sufficient to characterise such dyads. We provide a complete characterisation
by introducing a new invariant, the "fiber projectivity", and we present
examples that demonstrate its potential to explain hitherto not sufficiently
well understood phenomena.

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The categories of this paper are: nucl-th
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The categories of this paper are: econ
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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: astro-ph
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The categories of this paper are: mtrl-th
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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: cmp-lg
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The categories of this paper are: hep-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: gr-qc
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The categories of this paper are: q-fin
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The categories of this paper are: chem-ph
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The categories of this paper are: stat
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The categories of this paper are: hep-th