二维流形上的黎曼度量与欧拉-点索刚体问题有关

52nd IEEE Conference on Decision and Control Pub Date : 2013-12-10 DOI:10.1109/CDC.2013.6760144

B. Bonnard, O. Cots, N. Shcherbakova

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引用次数: 1

摘要

Euler-Poinsot刚体问题是SO(3)上的一个众所周知的左不变度量模型。本文讨论了两个相关的简化二维模型的性质:三个耦合自旋系统的次黎曼度规和通过Serret-Andoyer约简与Euler-Poinsot问题相关的黎曼度规。我们明确地构造了雅可比场，解释了黎曼情况下共轭轨迹的结构，并给出了自旋动力学情况下的第一个数值结果。

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

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 Euler-Poinsot 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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52nd IEEE Conference on Decision and Control

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