Email this article Relation between Euler’s elasticae and sub-Riemannian geodesics on SE(2)
- Authors: Mashtakov A.1, Ardentov A.1, Sachkov Y.L.1
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Affiliations:
- Program Systems Institute of RAS
- Issue: Vol 21, No 7-8 (2016)
- Pages: 832-839
- Section: Nonlinear Dynamics & Mobile Robotics
- URL: https://ogarev-online.ru/1560-3547/article/view/218471
- DOI: https://doi.org/10.1134/S1560354716070066
- ID: 218471
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Abstract
In this note we describe a relation between Euler’s elasticae and sub-Riemannian geodesics on SE(2). Analyzing the Hamiltonian system of the Pontryagin maximum principle, we show that these two curves coincide only in the case when they are segments of a straight line.
About the authors
Alexey Mashtakov
Program Systems Institute of RAS
Author for correspondence.
Email: alexey.mashtakov@gmail.com
Russian Federation, Pereslavl-Zalessky, Yaroslavl Region, 152020
Andrei Ardentov
Program Systems Institute of RAS
Email: alexey.mashtakov@gmail.com
Russian Federation, Pereslavl-Zalessky, Yaroslavl Region, 152020
Yuri L. Sachkov
Program Systems Institute of RAS
Email: alexey.mashtakov@gmail.com
Russian Federation, Pereslavl-Zalessky, Yaroslavl Region, 152020
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