Reachable sets for contact sub-Lorentzian structures on {mathbb{R}^3} . Application to control affine systems on {mathbb{R}^3} with a scalar input

In this paper, we investigate the structure of reachable sets for general contact sub-Lorentzian metrics on $ {mathbb{R}^3} $ . In some particular cases, the presented method leads to explicit formulas for functions describing reachable sets. We also compute the image under exponential mapping and prove that the sub-Lorentzian distance is continuous for the mentioned structures. All presented results concerning reachable sets can be directly applied to generic control affine systems in $ {mathbb{R}^3} $ with a scalar input u and constraints |u|??????.