Alexey Mashtakov

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


Mashtakov A. P., Popov A. Y.
For the sub-Riemannian problem on the group of motions of Euclidean space we present explicit formulas for extremal controls in the special case where one of the initial momenta is fixed.
Keywords: sub-Riemannian geometry, special Euclidean motion group, extremal controls
Citation: Mashtakov A. P., Popov A. Y.,  Extremal Controls in the Sub-Riemannian Problem on the Group of Motions of Euclidean Space, Regular and Chaotic Dynamics, 2017, vol. 22, no. 8, pp. 949–954
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, vol. 21, nos. 7-8, pp. 832-839

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