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Reports (Research Report) Year : 2006

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.
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Dates and versions

inria-00113372 , version 1 (13-11-2006)
inria-00113372 , version 2 (13-11-2006)

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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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