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