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This article is cited in 14 scientific papers (total in 14 papers)
Realizing Nonholonomic Dynamics as Limit of Friction Forces
Jaap Eldering Universidade de São Paulo — ICMC, Avenida Trabalhador Sao-carlense 400, CEP 13566-590, Sao Carlos, SP, Brazil
Abstract:
The classical question whether nonholonomic dynamics is realized as limit of friction forces was first posed by Carathéodory. 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 an example. This approximation scheme offers a reduction in dimension and has potential use in applications.
Keywords:
nonholonomic dynamics, friction, constraint realization, singular perturbation theory, Lagrange mechanics.
Citation:
Jaap Eldering, “Realizing Nonholonomic Dynamics as Limit of Friction Forces”, Regul. Chaotic Dyn., 21:4 (2016), 390–409
Linking options:
https://www.mathnet.ru/eng/rcd85 https://www.mathnet.ru/eng/rcd/v21/i4/p390
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Abstract page: | 224 | References: | 30 |
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