Alexey Mashtakov

Address: Pereslavl-Zalessky, Yaroslavl Region, 152020 Russia

University: Program Systems Institute of RAS

Publications:

Mashtakov A. P., Popov A. Y.

Extremal Controls in the Sub-Riemannian Problem on the Group of Motions of Euclidean Space
2017, vol. 22, no. 8, pp. 949–954

Abstract

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

DOI:10.1134/S1560354717080044

Mashtakov A. P., Ardentov A. A., Sachkov Y. L.

Relation Between Euler’s Elasticae and Sub-Riemannian Geodesics on $SE(2)$
2016, vol. 21, nos. 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, nos. 7-8, pp. 832-839

DOI:10.1134/S1560354716070066

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