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Fecha
2016-05-01
Derechos de acceso
info:eu-repo/semantics/openAccess
Título de la revista
ISSN de la revista
Título del volumen
Editorial
American Institute of Mathematical Sciences
Citas
Resumen
Optimal control problems for underactuated mechanical systems can be seen as a higher-order variational problem subject to higher-order constraints (that is, when the Lagrangian function and the constraints depend on higher-order derivatives such as the acceleration, jerk or jounces). In this paper we discuss the variational formalism for the class of underactuated mechanical control systems when the configuration space is a trivial principal bundle and the construction of variational integrators for such mechanical control systems.
An interesting family of geometric integrators can be defined using discretizations of the Hamilton's principle of critical action. This family of geometric integrators is called variational integrators, being one of their main properties the preservation of geometric features as the symplecticity, momentum preservation and good behavior of the energy. We construct variational integrators for higher-order mechanical systems on trivial principal bundles and their extension for higher-order constrained systems, paying particular attention to the case of underactuated mechanical systems.
Descripción
The registered version of this article, first published in Journal of Computational Dynamics, is available online at the publisher's website: EDITOR, https://doi.org/10.3934/jcd.2015003
La versión registrada de este artículo, publicado por primera vez en Journal of Computational Dynamics, está disponible en línea en el sitio web del editor: EDITOR, https://doi.org/10.3934/jcd.2015003
La versión registrada de este artículo, publicado por primera vez en Journal of Computational Dynamics, está disponible en línea en el sitio web del editor: EDITOR, https://doi.org/10.3934/jcd.2015003
Categorías UNESCO
Palabras clave
Variational integrators, higher-order mechanics, underactuated systems, optimal control, discrete variational calculus, constrained mechanics
Citación
Colombo, L., Jiménez, F., & de Diego, D. M. (2015). Variational integrators for mechanical control systems with symmetries. Journal of Computational Dynamics, 2(2), 193-225. https://doi.org/10.3934/JCD.2015003
Centro
E.T.S. de Ingenieros Industriales
Departamento
Matemática Aplicada I