Relation Between Euler’s Elasticae and Sub-Riemannian Geodesics on $SE(2)$

2016, Volume 21, Numbers 7-8, pp. 832-839

Author(s): Mashtakov A. P., Ardentov A. A., Sachkov Y. L.

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.

Keywords: elastica, sub-Riemannian geodesic, group of rototranslations

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, Volume 21, Numbers 7-8, pp. 832-839

DOI: 10.1134/S1560354716070066

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