Realizing nonholonomic dynamics as limit of friction forces
| Autor: | Jaap Eldering |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Nonholonomic system
Singular perturbation media_common.quotation_subject 010102 general mathematics Mathematical analysis Perturbation (astronomy) 02 engineering and technology Dynamical Systems (math.DS) Infinity 01 natural sciences 020303 mechanical engineering & transports Mathematics (miscellaneous) 0203 mechanical engineering Convergence (routing) FOS: Mathematics Limit (mathematics) Mathematics - Dynamical Systems 0101 mathematics Differential (infinitesimal) Reduction (mathematics) 37J60 (Primary) 37D10 70F40 70H09 (Secondary) Mathematics media_common |
| DOI: | 10.48550/arxiv.1603.00369 |
| Popis: | 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. Comment: 23 pages, 8 figures. Version as accepted for publication with only minor changes |
| Databáze: | OpenAIRE |
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