Symplectic integrators in sub-Riemannian geometry: the Martinet case
Numerical Analysis
2007-05-23 v1
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.
Cite
@article{arxiv.math/0611380,
title = {Symplectic integrators in sub-Riemannian geometry: the Martinet case},
author = {Monique Chyba and Ernst Hairer and Gilles Vilmart},
journal= {arXiv preprint arXiv:math/0611380},
year = {2007}
}