• CN：11-2187/TH
  • ISSN：0577-6686
机械工程学报

机械工程学报 ›› 2015, Vol. 51 ›› Issue (13): 81-85.doi: 10.3901/JME.2015.13.081

• 机构学及机器人学研究进展——纪念张启先院士诞辰九十周年专辑 • 上一篇    下一篇

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线变换刚体运动矩阵的群表示方法

杨朔飞i1, 孙涛i1, 黄田i1, 戴建生i1, 2   

  1. 1.天津大学机构理论与装备设计教育部重点实验室
    2.伦敦大学国王学院 伦敦 WC2R 2LS 英国
  • 出版日期:2015-07-05 发布日期:2015-07-05
  • 基金资助:
    国家自然科学基金(51135008, 51205278)和天津市科技型企业技术创新(14C26211200362)资助项目

Group Representation of Line Transformation Matrix of a Rigid Body

YANG Shuofei1, SUN Taoi1, HUANG Tiani1, DAI Jianshengi1, 2   

  1. 1.Key Laboratory of Mechanism Theory and Equipment Design of Ministry of Education, Tianjin University;
    2.King’s College, University of London
  • Online:2015-07-05 Published:2015-07-05

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摘要： 研究刚体有限和瞬时运动线变换矩阵的群表示方法。利用刚体运动微分方程导出线变换瞬时运动与有限运动的指数积映射显式表达。借助群表示论研究线变换有限及瞬时运动矩阵集合与SE(3)及se(3)在运动合成方面的等价性，证明前者是后者的忠实表示，并揭示出这种表示与伴随表示间的同构关系。工作旨在将描述刚体有限和瞬时运动不同的方法统一在群表示论框架下。

关键词: 刚体运动描述, 群表示论, 线变换

Abstract: The group representation of the line transformation matrices of finite and instantaneous motions of a rigid body in 3D space is investigated. The exponential mapping from the instantaneous motion to the finite motion is developed in an explicit manner using the differential equation of line transformation. This is followed by a vigorous proof that the entire set of finite (instantaneous) motion matrices of the line transformation is a faithful representation of SE(3) (se(3)), which, in turn, is isomorphic with the adjoint representation of SE(3) (se(3)) itself. The merit of this work lies in that it allows different representations of finite and instantaneous motions of a rigid body to be unified under the framework of group representation theory.

Key words: description of rigid body motions, group representation theory, line transformation

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