Yuri L. Sachkov

Submitted

[99] Yu.L. Sachkov, E.F. Sachkova, Sub-Lorentzian distance and spheres on the Heisenberg group  

2023

[98] Yu. Sachkov, Lorentzian geometry in the Lobachevsky plane  
[97] Ю.Л. Сачков, Е.Ф. Сачкова, Анормальные траектории в субримановой (2,3,5,8)-задаче  
[96] Ю.Л. Сачков, Е.Ф. Сачкова, Сублоренцева задача на группе Гейзенберга  
[95] Yu. Sachkov, Left-invariant optimal control problems on Lie groups integrable in elliptic functions  

2022

[94] Ю.Л. Сачков, Субриманова сфера Картана  
[93] Yu. Sachkov, Left-invariant optimal control problems on Lie groups: classifications and problems integrable in elementary functions  

2021

[92] Yu. Sachkov, E. Sachkova, Abnormal set for (2,3,5,8)-distribution  
[91] Yu. Sachkov, Homogeneous sub-Riemannian geodesics on the group of motions of the plane  
[90] Yu. Sachkov, E. Sachkova, Carnot algebras and sub-Riemannian structures with the growth vector (2,3,5,6)  
[89] Yu. Sachkov, A. Popov, Sub-Riemannian Engel sphere  
[88] Sachkov, Y.L. Conjugate Time in the Sub-Riemannian Problem on the Cartan Group  
[87] Andrei Ardentov, Gil Bor, Enrico Le Donne, Richard Montgomery and Yuri Sachkov, Bicycle paths, elasticae and sub-Riemannian geometry  
[86] A.A. Ardentov, L.V. Lokutsievskiy, Yu.L. Sachkov, Extremals for a series of sub-Finsler problems with 2-dimensional control via convex trigonometry  

2020

[85] A.A. Ardentov, L.V. Lokutsievskiy, Y.L. Sachkov, Explicit Solutions for a Series of Optimization Problems with 2-Dimensional Control via Convex Trigonometry
[84] Yu. Sachkov , E. F. Sachkova, The structure of abnormal extremals in a sub-Riemannian problem with growth vector (2, 3, 5, 8)  
[83] Ю.Л.Сачков, Сопряженные точки в обобщенной задаче Дидоны  
[82] Ю.Л. Сачков, Периодические оптимальные по быстродействию управления на двухступенных свободных нильпотентных группах Ли  
[81] Yu. Sachkov, Introduction to geometric control   
[80] Yu. L. Sachkov, Periodic controls in step 2 strictly convex sub-Finsler problems  

2019

[79] Yu. L.Sachkov, E. F.Sachkova, Symmetries and Parameterization of Abnormal Extremals in the Sub-Riemannian Problem with the Growth Vector (2, 3, 5, 8)  
[78] Ардентов А.А., Сачков Ю.Л., Субфинслеровы структуры на группе Энгеля  
[77] Andrei A. Ardentov, Enrico Le Donne, Yuri L. Sachkov, Sub-Finsler Geodesics on the Cartan Group  
[76] Ардентов А.А., Сачков Ю.Л., Субфинслерова задача на группе Картана  
[75] Ардентов А.А., Э. Ле Донне, Сачков Ю.Л., Экстремальные траектории в субфинслеровой задаче на группе Картана  

2018

[74] A. V. Podobryaev, Yu. L. Sachkov, Symmetric riemannian problem on the group of proper isometries of hyperbolic plane
[73] А. А. Ардентов, Ю. Л. Сачков, Т. Хуанг, К. Янг, “Экстремальные траектории в сублоренцевой задаче на группе Энгеля”  
[72] Yu. L. Sachkov, Optimal bang-bang trajectories in sub-Finsler problem on the Cartan group  
[71] Л.В. Локуциевский, Ю. Л. Сачков, Об интегрируемости по Лиувиллю субримановых задач на группах Карно глубины 4 и больше  
[70] A. A. Ardentov, Yu. L. Sachkov, Cut Locus in the Sub-Riemannian Problem on Engel Group
[69] A. A. Ardentov, Tiren Huang, Yu. L. Sachkov, Xiaoping Yang, Extremals in the Engel group with a sub-Lorentzian metric

2017

[68] A. V. Podobryaev, Yu. L. Sachkov, Left-Invariant Riemannian Problems on the Groups of Proper Motions of Hyperbolic Plane and Sphere
[67] E. Bekkers, R. Duits, A. Mashtakov, Yu. Sachkov. Vessel Tracking via Sub-Riemannian Geodesics on the Projective Line Bundle.  
[66] A. P. Mashtakov, Remco Duits, Yu. L. Sachkov, Erik Bekkers, I. Yu. Beschastnyi. Sub-Riemannian Geodesics in SO(3) with Application to Vessel Tracking in Spherical Images of Retina.   
[65] A. Mashtakov, R. Duits, Yu. Sachkov, E. J. Bekkers, I. Beschastnyi. Tracking of Lines in Spherical Images via Sub-Riemannian Geodesics in SO(3)   
[64] A. A. Ardentov, Yu. L. Sachkov, Maxwell Strata and Cut Locus in the Sub-Riemannian Problem on the Engel Group  
[63] Y.A.Butt, A.I. Bhatti, Yu.L. Sachkov, Cut Locus and Optimal Synthesis in Sub-Riemannian Problem on the Lie Group SH(2)  
[62] Ю. Л. Сачков, Е.Ф. Сачкова, Вырожденные анормальные экстремали в субримановой задаче с вектором роста (2,3,5,8)  

2016

[61] A. V. Podobryaev, Yu. L. Sachkov, Cut locus of a left invariant Riemannian metric on SO(3) in the axisymmetric case
[60] A.P. Mashtakov, A.A. Ardentov, Yu.L. Sachkov, Relation between Euler's Elasticae and Sub-Riemannian Geodesics on SE(2)  
[59] Qihui Cai, Tiren Huang, Yu. L. Sachkov, Xiaoping Yang, Geodesics in the Engel group with a sub-Lorentzian metric  
[58] I.Yu. Beschastnyi, Yu.L. Sachkov. Sub-Riemannian and almost-Riemannian geodesics on SO(3) and $S^2$   
[57] Ya. A. Butt, Yu. L. Sachkov, A.I. Bhatti, Maxwell strata and conjugate points in the sub-Riemannian problem on the Lie group SH(2)  

2015

[56] A. P. Mashtakov, Yu. L. Sachkov, Superintegrability of Sub-Riemannian Problems on Unimodular 3D Lie Groups   
[55] J.-P. Gauthier, Yu. L. Sachkov. On the free Carnot (2, 3, 5, 8) group  
[54] A. A. Ardentov, Yu. L. Sachkov, Cut time in sub-Riemannian problem on Engel group  

2014

[53] A.P. Mashtakov, Yu.L. Sachkov, Integrability of left-invariant sub-Riemannian structures on the special linear group $SL_2(R)$   
[52] Yu. L. Sachkov, E. L. Sachkova, Exponential mapping in Euler's elastic problem  
[51] U. Boscain, R. Duits, F. Rossi, Yu. L. Sachkov, Curve cuspless reconstruction via sub-Riemannian geometry  
[50] U. Boscain, R. Duits, F. Rossi, Yu. L. Sachkov, Association fields via cuspless sub-Riemannian geodesics in SE(2)  
[49] Ya. A. Butt, Yu. L. Sachkov, A. I. Bhatti, Parametrization of Extremal Trajectories in Sub-Riemannian Problem on Group of Motions of Pseudo Euclidean Plane  

2013

[48] M.G. Dmitriev, Yu.L. Sachkov, Optimal Control Problem Related to the Reconstruction of a Defective Curve  
[47] A. P. Mashtakov, A. A. Ardentov, Yu. L. Sachkov, Parallel algorithm and software for image inpainting via sub-Riemannian minimizers on the group of rototranslations  
[46] A. A. Ardentov, Yu. L. Sachkov, Conjugate points in nilpotent sub-Riemannian problem on the Engel group  

2012

[45] Ю. Л. Сачков, А. А. Ардентов, И. Ю. Бесчастный, А. П. Маштаков, Интерфейс для исследования субримановых геодезических на трехмерных группах Ли
[44] Yu.L. Sachkov, Closed Euler Elasticae  
[43] A. A. Ardentov, I. Yu. Beschatnyi, A. P. Mashtakov, A. Yu. Popov, Yu. L. Sachkov, E. F. Sachkova, Algorithms for evaluation position and orientation of UAV  

2011

[42] A. P. Mashtakov, Yu. L. Sachkov, Extremal trajectories and the asymptotics of the Maxwell time in the problem of the optimal rolling of a sphere on a plane   
[41] Yu. L. Sachkov, Cut locus and optimal synthesis in the sub-Riemannian problem on the group of motions of a plane  
[40] A.A. Ardentov, Yu.L. Sachkov, Extremal trajectories in a nilpotent sub-Riemannian problem on the Engel group   
[39] A. A. Ardentov, Yu. L. Sachkov, Antropomorphic recovery of corrupted images via methods of sub-Riemannian geometry  

2010

[38] Yu. L. Sachkov, Conjugate and cut time in the sub-Riemannian problem on the group of motions of a plane  
[37] I. Moiseev, Yu. L. Sachkov, Maxwell strata in sub-Riemannian problem on the group of motions of a plane  
[36] Yu. L. Sachkov, Maxwell strata and symmetries in the problem of optimal rolling of a sphere over a plane  
[35] Yu. L. Sachkov, A. A. Ardentov, A. P. Mashtakov, Parallel algorithm and software for recovery of isophotes for corrupted images  
[34] Yu. L. Sachkov, S. V. Levyakov, Stability of inflectional elasticae centered at vertices or inflection points   

2009

[33] Ю. Л. Сачков, А. А. Ардентов, А. П. Маштаков, Конструктивное решение задачи управления на основе метода нильпотентной аппроксимации  
[32] Yu.L. Sachkov, A.A. Ardentov, Parallel algorithms and programs for modelling of euler elasticae
[31] Yu. L. Sachkov, A. A. Ardentov, V. M. Kasimov, A. P. Mashtakov, Reconstruction of images via variational principle
[30] A. A. Ardentov, Yu. L. Sachkov, Solution to Euler’s elastic problem   

2008

[29] V.I. Gurman, Yu.L. Sachkov. Representation and realization of the generalized solutions of the unlimited-locus controllable systems
[28] Yu. L. Sachkov, Conjugate points in Euler's elastic problem  
[27] Yu. L. Sachkov, Maxwell strata in Euler's elastic problem  

2007

[26] Ю.Л. Сачков, Управляемость и симметрии инвариантных систем на группах Ли и однородных пространствах  
[25] Yu. L. Sachkov, Control theory on Lie groups   
[24] Yu. L. Sachkov, Optimality of Euler's elasticae  

2006

[23] Yu. L. Sachkov, Complete description of the Maxwell strata in the generalized Dido problem   
[22] Yu.L. Sachkov, The Maxwell set in the generalized Dido problem   
[21] Yu.L. Sachkov, Discrete symmetries in generalized Dido's problem   

2005

[20] A.A. Agrachev, Yu.L. Sachkov, Control theory from the geometric viewpoint   

2004

[19] A.A. Agrachev, Yu. L. Sachkov, Control theory from the geometric viewpoint  
[18] Yu. L. Sachkov, Symmetries of flat rank two distributions and sub-Riemannian Structures  

2003

[17] Yu. L. Sachkov, Exponential map in the generalized Dido problem  

2001

[16] A.A. Agrachev, Yu. L. Sachkov, Optimal control problem for a nonlinear driftless 5-dimensional system with 2 inputs  

2000

[15] Yu. L. Sachkov, Classification of controllable systems on low-dimensional solvable Lie groups  
[14] Yu. L. Sachkov, Controllability of Invariant Systems on Lie Groups and Homogeneous Spaces   

1999

[13] A.A. Agrachev, Yu. L. Sachkov, An Intrinsic Approach to the Control of Rolling Bodies  
[12] Yu. L. Sachkov, Survey on Controllability of Invariant Systems on Solvable Lie Groups  

1998

[11] Yu. L. Sachkov, On Invariant Orthants of Bilinear Systems  

1997

[10] Yu. L. Sachkov, Controllability of Right-Invariant Systems on Solvable Lie Groups  
[9] Yu. L. Sachkov, On Positive Orthant Controllability of Bilinear Systems in Small Codimensions
[8] Yu. L. Sachkov, Controllability of Affine Right-Invariant Systems on Solvable Lie Groups  

1996

[7] Yu. L. Sachkov, Controllability of Hypersurface and Solvable Invariant Systems  

1995

[6] Yu. L. Sachkov, Invariant Orthants of Bilinear Systems
[5] Yu. L. Sachkov, Positive Orthant Controllability of Single-input Bilinear Systems  

1993

[4] Yu. L. Sachkov, Invariant Orthants of Bilinear Systems
[3] Yu. L. Sachkov, Positive Orthant Controllability of 2-dimensional and 3-dimensional Bilinear Systems

1991

[2] Yu. L. Sachkov, Invariant Domains of 3-dimensional Bilinear Systems
[1] Yu. L. Sachkov, Controllability of 3-dimensional Bilinear Systems