11 citations · 20 across the 8 of their papers we have counts for
8 papers
Explicit formulas for extremals in sub-Lorentzian and Finsler problems on 2- and 3-dimensional Lie groups
E. A. Ladeishchikov, L. V. Lokutsievskiy, N. V. Prilepin
In this paper, we consider the problem of finding geodesics in a series of left-invariant problems endowed with sub-Lorentzian and Finsler structures. Explicit formulas for extrema…
Finsler and sub-Finsler geodesics with chattering
L. V. Lokutsievskiy, M. I. Zelikin
In this paper, we provide examples of Finsler and sub-Finsler manifolds whose geodesics exhibit chattering, that is, a countable number of switches over an arbitrarily small time i…
Asymptotic control theory for a closed string II
Lev Lokutsievskiy, Alexander Ovseevich
We develop an asymptotical control theory for one of the simplest distributed (infinite dimensional) oscillating systems, namely, for a closed string under a bounded load applied t…
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…
The analytical solution to Newton's aerodynamic problem in the class of bodies with vertical plane of symmetry and developable side boundary
L. V. Lokutsievskiy, M. I. Zelikin
The method of Hessian measures is used to find the differential equation that defines the optimal shape of nonrotationally symmetric bodies with minimal resistance moving in a rare…
Convex trigonometry with applications to sub-Finsler geometry
L. V. Lokutsievskiy
A new convenient method of describing flat convex compact sets is proposed. It generalizes classical trigonometric functions and . Apparently, this method may be very…
Hessian measures in the aerodynamic Newton problem
L. V. Lokutsievskiy, M. I. Zelikin
Simple natural proofs of all known results regarding the aerodynamic Newton problem are obtained. Additional new theorems and new promising formulas in terms of Hessian measures ar…
Homotopy types of group lattices
I. P. Kramarev, L. V. Lokutsievskiy
In this article we study group lattices using the ideas by K.S.Brown and D.Quillen of associating a certain topological space to a partially ordered set. We determine the exact hom…