Title: Relation between Euler's Elasticae and Sub-Riemannian Geodesics on SE(2)

Authors: A.P. Mashtakov, A.A. Ardentov, Yu.L. Sachkov

Journal title: Regular and Chaotic Dynamics

Year: 2016

Issue: 7-8

Volume: 21

Pages: 832-839

Citation:

Mashtakov A. P.,  Ardentov A. A.,  Sachkov Y. L., Relation Between Euler’s Elasticae and Sub-Riemannian Geodesics on SE(2), Regular and Chaotic Dynamics, 2016, vol. 21, no. 7-8, pp. 832-839

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.

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