Abstract
We demonstrate how the novel approach to the local geometry of structures of nonholonomic nature, originated by Andrei Agrachev, works for rank 2 distributions of maximal class in ℝn with additional structures such as affine control systems with one input spanning these distributions, sub-(pseudo)Riemannian structures etc. In contrast to the case of an arbitrary rank 2 distribution without additional structures, in the considered cases each abnormal extremal (of the underlying rank 2 distribution) possesses a distinguished parametrization. This fact allows one to construct the canonical frame on a (2n−3)-dimensional for arbitrary n ≥ 5. The moduli spaces of the most symmetric models are described as well.
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Doubrov, B., Zelenko, I. (2014). On geometry of affine control systems with one input. In: Stefani, G., Boscain, U., Gauthier, JP., Sarychev, A., Sigalotti, M. (eds) Geometric Control Theory and Sub-Riemannian Geometry. Springer INdAM Series, vol 5. Springer, Cham. https://doi.org/10.1007/978-3-319-02132-4_9
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DOI: https://doi.org/10.1007/978-3-319-02132-4_9
Publisher Name: Springer, Cham
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