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2013
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# Alexey Mashtakov

Pereslavl-Zalessky, Yaroslavl Region, 152020 Russia
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, 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