Solving Nonholonomic Systems with the Tau Method
| Autor: | José Matos, Alexandra Gavina, Paulo B. Vasconcelos |
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| Rok vydání: | 2019 |
| Předmět: |
Nonholonomic system
Transversality business.industry Computer science lcsh:T57-57.97 lcsh:Mathematics Applied Mathematics General Engineering Motion (geometry) lcsh:QA1-939 Optimal control lcsh:QA75.5-76.95 nonholonomic systems Computational Mathematics Lanczos resampling Maximum principle Software lcsh:Applied mathematics. Quantitative methods Applied mathematics lcsh:Electronic computers. Computer science Boundary value problem Tau method business |
| Zdroj: | Mathematical and Computational Applications Volume 24 Issue 4 Mathematical and Computational Applications, Vol 24, Iss 4, p 91 (2019) |
| ISSN: | 2297-8747 |
| DOI: | 10.3390/mca24040091 |
| Popis: | A numerical procedure based on the spectral Tau method to solve nonholonomic systems is provided. Nonholonomic systems are characterized as systems with constraints imposed on the motion. The dynamics is described by a system of differential equations involving control functions and several problems that arise from nonholonomic systems can be formulated as optimal control problems. Applying the Pontryagins maximum principle, the necessary optimality conditions along with the transversality condition, a boundary value problem is obtained. Finally, a numerical approach to tackle the boundary value problem is required. Here we propose the Lanczos spectral Tau method to obtain an approximate solution of these problems exploiting the Tau toolbox software library, which allows for ease of use as well as accurate results. |
| Databáze: | OpenAIRE |
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