On the relation between the exponential of real matrices and that of dual matrices

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters Pub Date : 2025-01-16 DOI:10.1016/j.aml.2025.109466

Chengdong Liu, Yimin Wei, Pengpeng Xie

引用次数: 0

Abstract

Dual number matrices play a significant role in engineering applications such as kinematics and dynamics. The matrix exponential is ubiquitous in screw-based kinematics. In this paper, we develop an explicit formula for the dual matrix exponential. The result is closely related to the Fréchet derivative, which can be formed by the standard part and dual part of the original matrix. We only need to compute the exponential of a real matrix. Then, we give a formula of computing the dual quaternion matrix exponential. Our results are illustrated through a practical example from robotic kinematics.

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实矩阵指数与对偶矩阵指数的关系

双数矩阵在运动学和动力学等工程应用中发挥着重要作用。矩阵指数在基于螺杆的运动学中无处不在。在本文中，我们为对偶矩阵指数建立了一个明确的公式。其结果与弗雷谢特导数密切相关，后者可由原始矩阵的标准部分和对偶部分构成。我们只需计算实矩阵的指数。然后，我们给出了计算对偶四元数矩阵指数的公式。我们将通过一个机器人运动学的实际例子来说明我们的结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied Mathematics Letters 数学-应用数学

CiteScore

7.70

自引率

5.40%

发文量

347

审稿时长

10 days

期刊介绍： The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.