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Solving Nonholonomic Systems with the Tau Method

Laboratório Engenharia Matemática, Instituto Superior Engenharia Porto, R. Dr. António Bernardino de Almeida 431, 4200-072 Porto, Portugal
Centro de Matemática, Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal
Faculdade de Economia, Universidade do Porto, Rua Dr. Roberto Frias, s/n, 4200-464 Porto, Portugal
Author to whom correspondence should be addressed.
Math. Comput. Appl. 2019, 24(4), 91;
Received: 27 September 2019 / Revised: 16 October 2019 / Accepted: 17 October 2019 / Published: 19 October 2019
(This article belongs to the Special Issue Numerical and Symbolic Computation: Developments and Applications)
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. View Full-Text
Keywords: Tau method; nonholonomic systems Tau method; nonholonomic systems
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MDPI and ACS Style

Gavina, A.; Matos, J.M.A.; Vasconcelos, P.B. Solving Nonholonomic Systems with the Tau Method. Math. Comput. Appl. 2019, 24, 91.

AMA Style

Gavina A, Matos JMA, Vasconcelos PB. Solving Nonholonomic Systems with the Tau Method. Mathematical and Computational Applications. 2019; 24(4):91.

Chicago/Turabian Style

Gavina, Alexandra, José M.A. Matos, and Paulo B. Vasconcelos 2019. "Solving Nonholonomic Systems with the Tau Method" Mathematical and Computational Applications 24, no. 4: 91.

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