6 papers
Cut time in the sub-Riemannian problem on the Cartan group
Andrei Ardentov, Eero Hakavuori
We study the sub-Riemannian structure determined by a left-invariant distribution of rank 2 on a step 3 Carnot group of dimension 5. We prove the conjectured cut times of Y. Sachko…
Bicycle paths, elasticae and sub-Riemannian geometry
Andrey Ardentov, Gil Bor, Enrico Le Donne +2
We relate the sub-Riemannian geometry on the group of rigid motions of the plane to `bicycling mathematics'. We show that this geometry's geodesics correspond to bike paths whose f…
Extremals for a series of sub-Finsler problems with 2-dimensional control via convex trigonometry
A. A. Ardentov, L. V. Lokutsievskiy, Yu. L. Sachkov
We consider a series of optimal control problems with 2-dimensional control lying in an arbitrary convex compact set . The considered problems are well studied for the case when…
Sub-Finsler geodesics on the Cartan group
A. Ardentov, E. Le Donne, Yu. Sachkov
This paper is a continuation of the work by the same authors on the Cartan group equipped with the sub-Finsler norm. We start by giving a detailed presentation of the…
A sub-Finsler problem on the Cartan group
A. Ardentov, E. Le Donne, Yu. Sachkov
In this paper we study a sub-Finsler geometric problem on the free-nilpotent group of rank 2 and step 3. Such a group is also called Cartan group and has a natural structure of Car…
Conjugate points in nilpotent sub-Riemannian problem on the Engel group
A. A. Ardentov, Yu. L. Sachkov
The left-invariant sub-Riemannian problem on the Engel group is considered. This problem is very important as nilpotent approximation of nonholonomic systems in four-dimensional sp…