Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Covariant Time Derivatives for Dynamical Systems   We present a unified derivation of covariant time derivatives, which
transform as tensors under a time-dependent coordinate change. Such derivatives
are essential for formulating physical laws in a frame-independent manner.
Three specific derivatives are described: convective, corotational, and
directional. The covariance is made explicit by working in arbitrary
time-dependent coordinates, instead of restricting to Eulerian (fixed) or
Lagrangian (material) coordinates. The commutator of covariant time and space
derivatives is interpreted in terms of a time-curvature that shares many
properties of the Riemann curvature tensor, and reflects nontrivial
time-dependence of the metric.

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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
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The categories of this paper are: adap-org
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The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
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The categories of this paper are: quant-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: supr-con
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The categories of this paper are: q-bio
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The categories of this paper are: acc-phys
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
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The categories of this paper are: cond-mat
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The categories of this paper are: patt-sol