Euler-Rodrigues formula variations, quaternion conjugation and intrinsic connections
Euler-Rodrigues formula variations, quaternion conjugation and intrinsic connections
复制标题
欧拉-罗德里格斯公式变体、四元数共轭和内在联系
DOI：
10.1016/j.mechmachtheory.2015.03.004
复制
发表时间：
2015-10-01
影响因子：
5.2
通讯作者：
Dai, Jian S.
中科院分区：
文献类型：
--
作者：
Dai, Jian S.
本文回顾了旋转的轴角表示中的欧拉-罗德里格斯公式，研究了它在向量、四元数和李群等不同数学形式中的变化和推导，并探讨了它们之间的内在联系。给出了泰勒级数展开式中的欧拉-罗德里格斯公式，并特别讨论了它作为李代数的指数映射的应用。然后通过四元数共轭证明了欧拉-罗德里格斯参数与欧拉-罗德里格斯公式之间的联系，并给出了四元数共轭与李群的伴随作用之间的等价性。本文为欧拉-罗德里格斯公式及其变式和它们之间的联系以及它们在刚体运动学、动力学和计算机图形学中的应用提供了丰富的参考。(C)2015年提交人。爱思唯尔有限公司出版。
This paper reviews the Euler-Rodrigues formula in the axis-angle representation of rotations, studies its variations and derivations in different mathematical forms as vectors, quaternions and Lie groups and investigates their intrinsic connections. The Euler-Rodrigues formula in the Taylor series expansion is presented and its use as an exponential map of Lie algebras is discussed particularly with a non-normalized vector. The connection between Euler-Rodrigues parameters and the Euler-Rodrigues formula is then demonstrated through quaternion conjugation and the equivalence between quaternion conjugation and an adjoint action of the Lie group is subsequently presented. The paper provides a rich reference for the Euler-Rodrigues formula, the variations and their connections and for their use in rigid body kinematics, dynamics and computer graphics. (C) 2015 The Author. Published by Elsevier Ltd.