Cargando...
Fecha
2016-06-23
Derechos de acceso
info:eu-repo/semantics/openAccess
Título de la revista
ISSN de la revista
Título del volumen
Editorial
Springer
Citas
Resumen
A new method is proposed to numerically integrate a dynamical system on a manifold such that the trajectory stably remains on the manifold and preserves the first integrals of the system. The idea is that given an initial point in the manifold we extend the dynamics from the manifold to its ambient Euclidean space and then modify the dynamics outside the intersection of the manifold and the level sets of the first integrals containing the initial point such that the intersection becomes a unique local attractor of the resultant dynamics. While the modified dynamics theoretically produces the same trajectory as the original dynamics, it yields a numerical trajectory that stably remains on the manifold and preserves the first integrals. The big merit of our method is that the modified dynamics can be integrated with any ordinary numerical integrator such as Euler or Runge–Kutta. We illustrate this method by applying it to three famous problems: the free rigid body, the Kepler problem and a perturbed Kepler problem with rotational symmetry. We also carry out simulation studies to demonstrate the excellence of our method and make comparisons with the standard projection method, a splitting method and Störmer–Verlet schemes.
Descripción
The registered version of this article, first published in Journal of Nonlinear Science, is available online at the publisher's website: EDITOR, https://doi.org/10.1007/S00332-016-9316-7
La versión registrada de este artículo, publicado por primera vez en Journal of Nonlinear Science, está disponible en línea en el sitio web del editor: EDITOR, https://doi.org/10.1007/S00332-016-9316-7
La versión registrada de este artículo, publicado por primera vez en Journal of Nonlinear Science, está disponible en línea en el sitio web del editor: EDITOR, https://doi.org/10.1007/S00332-016-9316-7
Categorías UNESCO
Palabras clave
Citación
Chang, D. E., Jiménez, F., & Perlmutter, M. (2016). Feedback Integrators. Journal of Nonlinear Science, 26(6), 1693-1721. https://doi.org/10.1007/S00332-016-9316-7
Centro
E.T.S. de Ingenieros Industriales
Departamento
Matemática Aplicada I