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2013
Impact Factor

Alexey Mashtakov

Pereslavl-Zalessky, Yaroslavl Region, 152020 Russia
Program Systems Institute of RAS

Publications:

Mashtakov A. P., Ardentov A. A., Sachkov Y. L.
Relation Between Euler’s Elasticae and Sub-Riemannian Geodesics on $SE(2)$
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.
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, vol. 21, no. 7-8, pp. 832-839
DOI:10.1134/S1560354716070066

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