Riemannian metrics on 2D manifolds related to the Euler-Poinsot rigid body problem

被引：0
|
作者：
Bonnard, Bernard [1 ]
Cots, Olivier [2 ]
Shcherbakova, Nataliya [3 ]
机构：
[1] Univ Bourgogne, Inst Math Bourgogne, F-21078 Dijon, France
[2] INRIA Sophia Antipolis Mediterranee, F-06902 Sophia Antipolis, France
[3] Univ Toulouse, INPT, UPS, Lab Genie Chim, F-31432 Toulouse, France
来源：
2013 IEEE 52ND ANNUAL CONFERENCE ON DECISION AND CONTROL (CDC) | 2013年
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中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
The Euler-Poinsot rigid body problem is a well known model of left-invariant metrics on SO (3). In the present paper we discuss the properties of two related reduced 2D models: the sub-Riemanian metric of a system of three coupled spins and the Riemannian metric associated to the EulerPoinsot problem via the Serret-Andoyer reduction. We explicitly construct Jacobi fields and explain the structure of conjugate loci in the Riemannian case and give the first numerical results for the spin dynamics case.
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页码：1804 / 1809
页数：6
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