Maxwell Strata and Cut Locus in the Sub-Riemannian Problem on the Engel Group
نویسندگان
چکیده
منابع مشابه
Maxwell 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,...
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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 ...
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چکیده ندارد.
15 صفحه اولConjugate 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...
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ژورنال
عنوان ژورنال: Regular and Chaotic Dynamics
سال: 2017
ISSN: 1560-3547,1468-4845
DOI: 10.1134/s1560354717080020