Symplectic integrators in sub-Riemannian geometry: the Martinet case

Monique Chyba; Ernst Hairer; Gilles Vilmart

Symplectic integrators in sub-Riemannian geometry: the Martinet case

Monique Chyba ¹ Ernst Hairer ² Gilles Vilmart ^{2, 3}

1 Department of Mathematics [Hawaii]

2 Section de mathématiques [Genève]

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.

Keywords : backward error analysis sub-Riemannian geometry Martinet abnormal geodesic symplectic integrator backward error analysis.

Type de document :

Rapport

[Research Report] RR-6017, INRIA. 2006, pp.10

Domaine :

Mathématiques [math] / Analyse numérique [math.NA]

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https://hal.inria.fr/inria-00113372
Contributeur : Rapport de Recherche Inria <>
Soumis le : lundi 13 novembre 2006 - 18:02:05
Dernière modification le : vendredi 16 novembre 2018 - 01:30:03
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Symplectic integrators in sub-Riemannian geometry: the Martinet case

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Symplectic integrators in sub-Riemannian geometry: the Martinet case

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