33 citations · 53 across the 11 of their papers we have counts for
7 papers · 1 filter
Liouville integrability in a four-dimensional model of the visual cortex
Ivan Galyaev, Alexey Mashtakov
We consider a natural extension of the Petitot-Citti-Sarti model of the primary visual cortex. In the extended model, the curvature of contours is taking into account such that occ…
Time minimization problem on the group of motions of a plane with admissible control in a half-disk
Alexey Mashtakov
We study a time minimization problem on the group of motions of a plane with admissible control in a half-disk. The considered control system describes a model of a car that can mo…
Extremal Controls in the Sub-Riemannian Problem on the Group of Motions of Euclidean Space
Alexey Mashtakov, Anton Popov
For the sub-Riemannian problem on the group of motions of Euclidean space we present explicit formulas for extremal controls in a special case, when one of the initial momenta is f…
Vessel Tracking via Sub-Riemannian Geodesics on
E. J. Bekkers, R. Duits, A. Mashtakov +1
We study a data-driven sub-Riemannian (SR) curve optimization model for connecting local orientations in orientation lifts of images. Our model lives on the projective line bundle…
Relation between Euler's Elasticae and Sub-Riemannian Geodesics on SE(2)
Alexey Mashtakov, Andrei Ardentov, Yuri Sachkov
In this note we describe a relation between Euler's elasticae and sub-Riemannian geodesics on SE(2). Analyzing the Hamiltonian system of Pontryagin maximum principle we show that t…
Superintegrability of Sub-Riemannian Problems on Unimodular 3D Lie Groups
Alexey P. Mashtakov, Yuri L. Sachkov
Left-invariant sub-Riemannian problems on unimodular 3D Lie groups are considered. For the Hamiltonian system of Pontryagin maximum principle for sub-Riemannian geodesics, the Liou…
Asymptotics of Maxwell time in the plate-ball problem
A. P. Mashtakov, A. Yu. Popov
The problem on rolling of a sphere on a plane without slipping or twisting is considered. One should roll the sphere from one contact configuration to another so that the length of…