Symplectic integrators in sub-Riemannian geometry: the Martinet case

Details Symplectic integrators in sub-Riemannian geometry: the Martinet case Symplectic integrators in sub-Riemannian geometry: the Martinet case

2006-11-13

arxiv.org/abs/math/0611380v1

Mathematics

Numerical Analysis

Scientific paper

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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