Cut time in sub-riemannian problem on engel group
نویسندگان
چکیده
منابع مشابه
Conjugate and Cut Time in the Sub-riemannian Problem on the Group of Motions of a Plane
The left-invariant sub-Riemannian problem on the group of motions (rototranslations) of a plane SE(2) is studied. Local and global optimality of extremal trajectories is characterized. Lower and upper bounds on the first conjugate time are proved. The cut time is shown to be equal to the first Maxwell time corresponding to the group of discrete symmetries of the exponential mapping. Optimal syn...
متن کاملCut Locus and Optimal Synthesis in the Sub-riemannian Problem on the Group of Motions of a Plane
The left-invariant sub-Riemannian problem on the group of motions (rototranslations) of a plane SE(2) is considered. In the previous works [Moiseev and Sachkov, ESAIM: COCV, DOI: 10.1051/cocv/2009004; Sachkov, ESAIM: COCV, DOI: 10.1051/cocv/2009031], extremal trajectories were defined, their local and global optimality were studied. In this paper the global structure of the exponential mapping ...
متن کاملParametrization of Extremal Trajectories in Sub-Riemannian Problem on Group of Motions of Pseudo Euclidean Plane
We consider the sub-Riemannian length optimization problem on the group of motions of hyperbolic plane i.e. the special hyperbolic group SH(2). The system comprises of left invariant vector fields with 2 dimensional linear control input and energy cost functional. We prove the global controllability of control distribution and use Pontryagin Maximum Principle to obtain the extremal control inpu...
متن کاملMaxwell Strata in Sub-riemannian Problem on the Group of Motions of a Plane
The left-invariant sub-Riemannian problem on the group of motions of a plane is considered. Sub-Riemannian geodesics are parameterized by Jacobi’s functions. Discrete symmetries of the problem generated by reflections of pendulum are described. The corresponding Maxwell points are characterized, on this basis an upper bound on the cut time is obtained. Mathematics Subject Classification. 49J15,...
متن کاملThe regularity problem for sub-Riemannian geodesics
One of the main open problems in sub-Riemannian geometry is the regularity of length minimizing curves, see [12, Problem 10.1]. All known examples of length minimizing curves are smooth. On the other hand, there is no regularity theory of a general character for sub-Riemannian geodesics. It was originally claimed by Strichartz in [15] that length minimizing curves are smooth, all of them being ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: ESAIM: Control, Optimisation and Calculus of Variations
سال: 2015
ISSN: 1292-8119,1262-3377
DOI: 10.1051/cocv/2015027