Relation between Euler's Elasticae and Sub-Riemannian Geodesics on SE(2)
Optimization and Control
2017-04-05 v1
Abstract
In this note we describe a relation between Euler's elasticae and sub-Riemannian geodesics on SE(2). Analyzing the Hamiltonian system of Pontryagin maximum principle we show that these two curves coincide only in the case when they are segments of a straight line.
Keywords
Cite
@article{arxiv.1609.03704,
title = {Relation between Euler's Elasticae and Sub-Riemannian Geodesics on SE(2)},
author = {Alexey Mashtakov and Andrei Ardentov and Yuri Sachkov},
journal= {arXiv preprint arXiv:1609.03704},
year = {2017}
}