Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An extension to the theory of controlled Lagrangians using the Helmholtz
  conditions   The Helmholtz conditions are necessary and sufficient conditions for a system
of second order differential equations to be variational, that is, equivalent
to a system of Euler-Lagrange equations for a regular Lagrangian. On the other
hand, matching conditions are sufficient conditions for a class of controlled
systems to be variational for a Lagrangian function of a prescribed type, known
as the controlled Lagrangian. Using the Helmholtz conditions we are able to
recover the matching conditions from [8]. Furthermore we can derive new
matching conditions for a particular class of mechanical systems. It turns out
that for this class of systems we obtain feedback controls that only depend on
the configuration variables. We test this new strategy for the inverted
pendulum on a cart and for the inverted pendulum on an incline.

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The categories of this paper are: cond-mat
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The categories of this paper are: cmp-lg
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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
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The categories of this paper are: plasm-ph
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The categories of this paper are: stat
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The categories of this paper are: hep-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: gr-qc
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The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci