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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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