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Symplectic integrators in sub-Riemannian geometry: the Martinet case

Monique Chyba 1 Ernst Hairer 2 Gilles Vilmart 2, 3
3 IPSO - Invariant Preserving SOlvers
IRMAR - Institut de Recherche Mathématique de Rennes, Inria Rennes – Bretagne Atlantique
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.
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https://hal.inria.fr/inria-00113372
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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

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Monique Chyba, Ernst Hairer, Gilles Vilmart. Symplectic integrators in sub-Riemannian geometry: the Martinet case. [Research Report] RR-6017, INRIA. 2006, pp.10. ⟨inria-00113372v2⟩

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