基于双四元数的高阶Cayley映射的刚体位移和运动最小参数化

IF 2.2 3区 综合性期刊 Q2 MULTIDISCIPLINARY SCIENCES Symmetry-Basel Pub Date : 2023-11-01 DOI:10.3390/sym15112011
Daniel Condurache, Ionuț Popa
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引用次数: 0

摘要

刚体位移数学模型是特殊欧几里得群SE(3)的李群。本文讨论了李代数SE(3)群。从se(3)到se(3)的标准指数映射是这些位移的自然参数化。在技术应用中,一个关键问题是流形SE(3)的向量最小参数化。本文给出了这类向量最小参数化的一般类的酉变形式。近年来,对偶代数已成为分析和计算刚体运动和位移特性的综合框架。基于对偶四元数的高阶分数阶Cayley变换,计算了高阶Rodrigues对偶向量和多个向量参数(由旋转情况扩展)。对于刚体运动描述,计算了对偶切线算子(对于任何矢量最小参数化)。本文给出了对偶运动方程初值问题的一种统一方法。
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A Minimal Parameterization of Rigid Body Displacement and Motion Using a Higher-Order Cayley Map by Dual Quaternions
The rigid body displacement mathematical model is a Lie group of the special Euclidean group SE (3). This article is about the Lie algebra se (3) group. The standard exponential map from se (3) onto SE (3) is a natural parameterization of these displacements. In technical applications, a crucial problem is the vector minimal parameterization of manifold SE (3). This paper presents a unitary variant of a general class of such vector parameterizations. In recent years, dual algebra has become a comprehensive framework for analyzing and computing the characteristics of rigid-body movements and displacements. Based on higher-order fractional Cayley transforms for dual quaternions, higher-order Rodrigues dual vectors and multiple vectorial parameters (extended by rotational cases) were computed. For the rigid body movement description, a dual tangent operator (for any vectorial minimal parameterization) was computed. This paper presents a unitary method for the initial value problem of the dual kinematic equation.
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来源期刊
Symmetry-Basel
Symmetry-Basel MULTIDISCIPLINARY SCIENCES-
CiteScore
5.40
自引率
11.10%
发文量
2276
审稿时长
14.88 days
期刊介绍: Symmetry (ISSN 2073-8994), an international and interdisciplinary scientific journal, publishes reviews, regular research papers and short notes. Our aim is to encourage scientists to publish their experimental and theoretical research in as much detail as possible. There is no restriction on the length of the papers. Full experimental and/or methodical details must be provided, so that results can be reproduced.
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