Non-holonomic equations for the normal extremals in geometric control theory
| Authors | |
|---|---|
| Year of publication | 2022 |
| Type | Article in Periodical |
| Magazine / Source | Journal of Geometry and Physics |
| MU Faculty or unit | |
| Citation | |
| Web | https://doi.org/10.1016/j.geomphys.2021.104395 |
| 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 |
| Description | 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. |
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