Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Realizing nonholonomic dynamics as limit of friction forces   The classical question whether nonholonomic dynamics is realized as limit of
friction forces was first posed by Carath\'eodory. It is known that, indeed,
when friction forces are scaled to infinity, then nonholonomic dynamics is
obtained as a singular limit.
  Our results are twofold. First, we formulate the problem in a differential
geometric context. Using modern geometric singular perturbation theory in our
proof, we then obtain a sharp statement on the convergence of solutions on
infinite time intervals. Secondly, we set up an explicit scheme to approximate
systems with large friction by a perturbation of the nonholonomic dynamics. The
theory is illustrated in detail by studying analytically and numerically the
Chaplygin sleigh as example. This approximation scheme offers a reduction in
dimension and has potential use in applications.

21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat