Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Novel Solution to the Frenet-Serret Equations   A set of equations is developed to describe a curve in space given the
curvature $\kappa$ and the angle of rotation $\theta$ of the osculating plane.
The set of equations has a solution (in terms of $\kappa$ and $\theta$) that
indirectly solves the Frenet-Serret equations, with a unique value of $\theta$
for each specified value of $\tau$. Explicit solutions can be generated for
constant $\theta$. The equations break down when the tangent vector aligns to
one of the unit coordinate vectors, requiring a reorientation of the local
coordinate system.

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The categories of this paper are: physics
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The categories of this paper are: dg-ga
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The categories of this paper are: mtrl-th
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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: nlin
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The categories of this paper are: cond-mat
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The categories of this paper are: gr-qc
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The categories of this paper are: acc-phys
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The categories of this paper are: eess
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-ex
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The categories of this paper are: stat
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The categories of this paper are: q-fin
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-lat