New developments on the geometric nonholonomic integrator
In this paper, we will discuss new developments regarding the geometric nonholonomic integrator (GNI) (Ferraro et al 2008 Nonlinearity 21 1911-28; Ferraro et al 2009 Discrete Contin. Dyn. Syst. (Suppl.) 220-9). GNI is a discretization scheme adapted to nonholonomic mechanical systems through a discr...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2015 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/77966 |
| Acceso en línea: | http://hdl.handle.net/11336/77966 |
| Access Level: | acceso abierto |
| Palabra clave: | 37j60 37m15 37n05 65p10 70-08 Affine Constraints Mathematics Subject Classification: 70f25 Discrete Variational Calculus Geometric Nonholonomic Integrator Nonholonomic Mechanics Reduction by Symmetries https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Sumario: | In this paper, we will discuss new developments regarding the geometric nonholonomic integrator (GNI) (Ferraro et al 2008 Nonlinearity 21 1911-28; Ferraro et al 2009 Discrete Contin. Dyn. Syst. (Suppl.) 220-9). GNI is a discretization scheme adapted to nonholonomic mechanical systems through a discrete geometric approach. This method was designed to account for some of the special geometric structures associated to a nonholonomic motion, like preservation of energy, preservation of constraints or the nonholonomic momentum equation. First, we study the GNI versions of the symplectic-Euler methods, paying special attention to their convergence behaviour. Then, we construct an extension of the GNI in the case of affine constraints. Finally, we generalize the proposed method to nonholonomic reduced systems, an important subclass of examples in nonholonomic dynamics. We illustrate the behaviour of the proposed method with the example of the inhomogeneous sphere rolling without slipping on a table. |
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