中文摘要：

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。

英文摘要：

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.