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@article{1799704, author = {Gover, A. Rod and Slovák, Jan}, article_number = {January}, doi = {http://dx.doi.org/10.1016/j.geomphys.2021.104395}, keywords = {Connections; Geometric control theory; Non-holonomic Riemannian geometry; Normal extremals; Sub-Riemannian geometry}, language = {eng}, issn = {0393-0440}, journal = {Journal of Geometry and Physics}, title = {Non-holonomic equations for the normal extremals in geometric control theory}, url = {https://doi.org/10.1016/j.geomphys.2021.104395}, volume = {171}, year = {2022} }
TY - JOUR ID - 1799704 AU - Gover, A. Rod - Slovák, Jan PY - 2022 TI - Non-holonomic equations for the normal extremals in geometric control theory JF - Journal of Geometry and Physics VL - 171 IS - January SP - 104395 EP - 104395 PB - Elsevier SN - 03930440 KW - Connections KW - Geometric control theory KW - Non-holonomic Riemannian geometry KW - Normal extremals KW - Sub-Riemannian geometry UR - https://doi.org/10.1016/j.geomphys.2021.104395 N2 - Applying the point of view of non-holonomic mechanics, we arrive at a new and simple system of equations for the normal sub-Riemannian geodesics. These use a partial connection that is canonically available, given a choice of complement to the distribution. We also describe conditions which, if satisfied, mean that even this choice of complement is determined canonically, and that this determines a distinguished connection on the tangent bundle. The geodesic equations obtained split into mutually driving horizontal and complementary parts. The method facilitates efficient choices of adapted coframes and reveals structures that are reminiscent of tractor calculi. We illustrate the features on examples, including some with non-constant symbols. ER -
GOVER, A. Rod and Jan SLOVÁK. Non-holonomic equations for the normal extremals in geometric control theory. \textit{Journal of Geometry and Physics}. Elsevier, 2022, vol.~171, January, p.~104395-104408. ISSN~0393-0440. Available from: https://dx.doi.org/10.1016/j.geomphys.2021.104395.
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