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Symplectic integrators in sub-Riemannian geometry: the Martinet case
Abstract : We compare the performances of symplectic and non-symplectic integrators for the computation of normal geodesics and conjugate points in sub-Riemannian geometry at the example of the Martinet case. For this case study we consider first the flat metric, and then a one parameter perturbation leading to non integrable geodesics. From our computations we deduce that near the abnormal directions a symplectic method is much more efficient for this optimal control problem. The explanation relies on the theory of backward error analysis in geometric numerical integration.
Cited literature [2 references]
https://hal.inria.fr/inria-00113372
Contributor : Rapport de Recherche Inria Connect in order to contact the contributor
Submitted on : Monday, November 13, 2006 - 6:02:05 PM
Last modification on : Wednesday, April 6, 2022 - 3:48:06 PM
Long-term archiving on: : Monday, September 20, 2010 - 5:18:16 PM
Contributor : Rapport de Recherche Inria Connect in order to contact the contributor
Submitted on : Monday, November 13, 2006 - 6:02:05 PM
Last modification on : Wednesday, April 6, 2022 - 3:48:06 PM
Long-term archiving on: : Monday, September 20, 2010 - 5:18:16 PM