Email this article Convex trigonometry with applications to sub-Finsler geometry
- Authors: Lokutsievskiy L.V.1,2
-
Affiliations:
- Steklov Mathematical Institute of Russian Academy of Sciences
- Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
- Issue: Vol 210, No 8 (2019)
- Pages: 120-148
- Section: Articles
- URL: https://journals.rcsi.science/0368-8666/article/view/142381
- DOI: https://doi.org/10.4213/sm9134
- ID: 142381
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Abstract
A new convenient method for describing flat convex compact sets and their polar sets is proposed. It generalizes the classical trigonometric functions $\sin$ and $\cos$. It is apparent that this method can be very useful for an explicit description of solutions of optimal control problems with two-dimensional control. Using this method a series of sub-Finsler problems with two-dimensional control lying in an arbitrary convex set $\Omega$ is investigated. Namely, problems on the Heisenberg, Engel, and Cartan groups and also Grushin's and Martinet's cases are considered. Particular attention is paid to the case when $\Omega$ is a convex polygon.Bibliography: 13 titles.
About the authors
Lev Vyacheslavovich Lokutsievskiy
Steklov Mathematical Institute of Russian Academy of Sciences; Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Email: lion.lokut@gmail.com
Doctor of physico-mathematical sciences, no status
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