English

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}
}
R2 v1 2026-06-22T15:47:59.189Z