Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Lagrangian Structure of Reduced Dynamics Under Virtual Holonomic
  Constraints   This paper investigates a class of Lagrangian control systems with $n$
degrees-of-freedom (DOF) and n-1 actuators, assuming that $n-1$ virtual
holonomic constraints have been enforced via feedback, and a basic regularity
condition holds. The reduced dynamics of such systems are described by a
second-order unforced differential equation. We present necessary and
sufficient conditions under which the reduced dynamics are those of a
mechanical system with one DOF and, more generally, under which they have a
Lagrangian structure. In both cases, we show that typical solutions satisfying
the virtual constraints lie in a restricted class which we completely
characterize.

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The categories of this paper are: q-bio
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ex
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The categories of this paper are: math-ph
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The categories of this paper are: physics
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The categories of this paper are: chem-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: quant-ph
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The categories of this paper are: q-alg
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The categories of this paper are: solv-int
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The categories of this paper are: plasm-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: supr-con