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2020 | OriginalPaper | Chapter

Closed Form of the Baker-Campbell-Hausdorff Formula for the Lie Algebra of Rigid Body Displacements

Authors : Daniel Condurache, Ioan-Adrian Ciureanu

Published in: Multibody Dynamics 2019

Publisher: Springer International Publishing

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Abstract

This paper demonstrates the existence of the closed form of the Baker-Campbell-Hausdorff (BCH) formula for the Lie algebra of rigid body displacement. For this, the structure of the Lie group of the rigid body displacements \( S{\mathbb{E}}_{3} \) and the properties of its algebra Lie https://static-content.springer.com/image/chp%3A10.1007%2F978-3-030-23132-3_37/MediaObjects/486143_1_En_37_Figa_HTML.png are used. Also, using the isomorphism between the Lie group \( S{\mathbb{E}}_{3} \) and the Lie group of the orthogonal dual tensors, a solution of this problem in dual algebra is given.

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Literature
1.
2.
Foulis, D.L.: The algebra of complex 2 × 2 matrices and a general closed Baker–Campbell–Hausdorff formula. J. Phys. A: Math. Theor. 50(30), 305204 (2017)MathSciNetCrossRef
3.
Lo, C.F.: Comment on ‘special-case closed form of the Baker–Campbell–Hausdorff formula’. J. Phys. A: Math. Theor. 49(21), 218001 (2016)MathSciNetCrossRef
4.
Matone, M.: Closed form of the Baker–Campbell–Hausdorff formula for the generators of semisimple complex Lie algebras. Eur. Phys. J. C 76, 610 (2016)CrossRef
5.
Van-Brunt, A., Visser, M.: Special-case closed form of the Baker-Campbell-Hausdorff formula. J. Phys. A: Math. Theor. 48(22), 225207 (2015)MathSciNetCrossRef
6.
7.
Chirikjian, G.S., Kyatkin, A.B.: Harmonic Analysis for Engineers and Applied Scientists, Updated and Expanded Edition Edition, p. 255. Courier Dover Publications, New York (2016)
8.
Park, J., Chung, W.-K.: Geometric integration on Euclidean group with application to articulated multibody systems. IEEE Trans. Rob. 21(5), 850–863 (2005)CrossRef
9.
Condurache, D., Ciureanu, I.-A.: Higher-order Cayley transforms for SE(3). New Adv. Mech. Mach. Sci. 57, 331–339 (2018)CrossRef
10.
Condurache, D., Burlacu, A.: Dual tensors based solutions for rigid body motion parameterization. Mech. Mach. Theory 74, 390–412 (2014)CrossRef
11.
Condurache, D., Burlacu, A.: Orthogonal dual tensor method for solving the AX = XB sensor calibration problem. Mech. Mach. Theory 104, 382–404 (2016)CrossRef
12.
Pennestrì, E., Valentini, P.P.: Linear dual algebra algorithms and their application to kinematics. Multibody Dyn.: Comput. Methods Appl. 12, 207–229 (2009)MathSciNetCrossRef
Metadata
Title
Closed Form of the Baker-Campbell-Hausdorff Formula for the Lie Algebra of Rigid Body Displacements
Authors
Daniel Condurache
Ioan-Adrian Ciureanu
Copyright Year
2020
Book
Multibody Dynamics 2019

Print ISBN: 978-3-030-23131-6

Electronic ISBN: 978-3-030-23132-3

Copyright Year: 2020

DOI
https://doi.org/10.1007/978-3-030-23132-3_37

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