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Fecha
2019-01-01
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
In this paper we investigate a variational discretization for the class of mechanical systems in presence of symmetries described by the action of a Lie group which reduces the phase space to a (non-trivial) principal bundle. By introducing a discrete connection we are able to obtain the discrete constrained higher-order Lagrange-Poincaré equations. These equations describe the dynamics of a constrained Lagrangian system when the Lagrangian function and the constraints depend on higher-order derivatives such as the acceleration, jerk or jounces. The equations, under some mild regularity conditions, determine a well defined (local) flow which can be used to define a numerical scheme to integrate the constrained higher-order Lagrange-Poincaré equations.
Optimal control problems for underactuated mechanical systems can be viewed as higher-order constrained variational problems. We study how a variational discretization can be used in the construction of variational integrators for optimal control of underactuated mechanical systems where control inputs act soley on the base manifold of a principal bundle (the shape space). Examples include the energy minimum control of an electron in a magnetic field and two coupled rigid bodies attached at a common center of mass.
Descripción
The registered version of this article, first published in Discrete and Continuous Dynamical Systems- Series A, is available online at the publisher's website: American Institute of Mathematical Sciences, https://doi.org/10.3934/dcds.2019013
La versión registrada de este artículo, publicado por primera vez en Discrete and Continuous Dynamical Systems- Series A, está disponible en línea en el sitio web del editor: American Institute of Mathematical Sciences, https://doi.org/10.3934/dcds.2019013
La versión registrada de este artículo, publicado por primera vez en Discrete and Continuous Dynamical Systems- Series A, está disponible en línea en el sitio web del editor: American Institute of Mathematical Sciences, https://doi.org/10.3934/dcds.2019013
Categorías UNESCO
Palabras clave
Variational integrators, discrete mechanical systems, discrete mechanical systems, LagrangePoincar´e equations, geometric integration, discrete variational calculus, ordinary differential equations, control of mechanical systems, reduction by symmetries
Citación
Bloch, A., Colombo, L., & Jiménez, F. (2019). The variational discretization of the constrained higher-order lagrange-poincaré equations. Discrete and Continuous Dynamical Systems- Series A, 39(1), 309-344. https://doi.org/10.3934/DCDS.2019013
Centro
E.T.S. de Ingenieros Industriales
Departamento
Matemática Aplicada I