On the relation between the exponential of real matrices and that of dual matrices
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 deriva...
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| Vydané v: | Applied mathematics letters Ročník 163; s. 109466 |
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01.04.2025
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| ISSN: | 0893-9659 |
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| 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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| AbstractList | 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. |
| ArticleNumber | 109466 |
| Author | Wei, Yimin Liu, Chengdong Xie, Pengpeng |
| Author_xml | – sequence: 1 givenname: Chengdong orcidid: 0009-0001-9578-4826 surname: Liu fullname: Liu, Chengdong email: 20307130110@fudan.edu.cn organization: School of Mathematical Sciences, Fudan University, Shanghai, 200433, PR China – sequence: 2 givenname: Yimin surname: Wei fullname: Wei, Yimin email: ymwei@fudan.edu.cn organization: School of Mathematical Sciences and Shanghai Key Laboratory of Contemporary Applied Mathematics, Fudan University, Shanghai, 200433, PR China – sequence: 3 givenname: Pengpeng surname: Xie fullname: Xie, Pengpeng email: xie@ouc.edu.cn organization: School of Mathematical Sciences, Ocean University of China, Qingdao, 266100, PR China |
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| Cites_doi | 10.1177/0278364920931948 10.1137/080716426 10.1112/plms/s1-4.1.381 10.1115/1.4043204 10.1016/j.mechmachtheory.2020.103861 10.1137/23M1556642 10.1115/1.4030588 10.1016/j.mechmachtheory.2020.103878 10.1109/IROS.2010.5650218 10.3390/sym16091142 10.1016/j.mechmachtheory.2020.104212 10.1115/1.4064576 10.1016/j.aml.2024.109144 10.1115/1.4028758 10.1137/24M1652234 10.1016/j.mechmachtheory.2005.04.004 10.1002/nla.2245 10.1007/BF01199824 10.1115/1.1737378 10.1080/03081081003739204 10.1016/j.cam.2024.116185 10.1016/j.cam.2009.11.032 10.1007/s10915-024-02561-x 10.1016/j.mechmachtheory.2020.104158 10.1016/j.mechmachtheory.2023.105566 10.1177/027836498900800505 10.1016/j.mechmachtheory.2022.105184 10.1016/0024-3795(95)00543-9 10.1016/S0094-114X(98)00049-4 10.1007/s40314-023-02565-7 |
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| SubjectTerms | Dual matrices Dual quaternion Fréchet derivative Kinematics Matrix exponential |
| Title | On the relation between the exponential of real matrices and that of dual matrices |
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