Geodesics in the sub-Riemannian problem on the group SO(3)

被引：3

作者：

Beschastnyi, I. Yu. ^{[1
]}

Sachkov, Yu. L. ^{[1
]}

机构：

[1] Russian Acad Sci, Program Syst Inst, Pereslavl Dist, Yaroslavl Oblas, Russia

来源：

SBORNIK MATHEMATICS | 2016年 / 207卷 / 07期

关键词：

sub-Riemannian geometry; almost Riemannian geometry; optimal control; geodesic curves; cut time; LIE-GROUPS; GEOMETRY; METRICS; MOTIONS; PLANE; SYSTEMS; S-3;

D O I：

10.1070/SM8555

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Geodesics of left-invariant sub-Riemannian structures are considered on the group SO(3). A complete description of periodic geodesics, their elementary properties, certain necessary conditions for minimality and estimates for the cut time and the diameter of the metric are presented.

引用

页码：915 / 941

页数：27

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