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Covariant Decomposition of the Three-Dimensional Rotations

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Intelligent Robotics and Applications (ICIRA 2014)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8918))

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Abstract

The main purpose of this paper is to provide an alternative representation for the generalized Euler decomposition (with respect to arbitrary axes) obtained in [2,3] by means of vector parameterization of the Lie group SO(3). The scalar (angular) parameters of the decomposition are explicitly written here as functions depending only on the contravariant components of the compound vector-parameter in the basis, determined by the three axes. We also consider the case of coplanar axes, in which the basis needs to be completed by a third vector and in particular, two-axes decompositions.

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Author information

Authors and Affiliations

  1. Institute of Mechanics, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Clementina D. Mladenova

  2. Civil Engineering and Geodesy, University of Architecture, Sofia, Bulgaria

    Danail S. Brezov

  3. Institute of Biophysics, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Ivaïlo M. Mladenov

Authors
  1. Clementina D. Mladenova
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  2. Danail S. Brezov
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  3. Ivaïlo M. Mladenov
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Editor information

Editors and Affiliations

  1. School of Mechanical and Automobile Engineering, South China University of Technology, Wushan Rd. 381, Tianhe District, 510641, Guangzhou, China

    Xianmin Zhang , Zhong Chen  & Nianfeng Wang ,  & 

  2. Group of Intelligent System and Biomedical Robotics, School of Creative Technologies, University of Portsmouth, Portsmouth, United Kingdom

    Honghai Liu

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© 2014 Springer International Publishing Switzerland

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Mladenova, C.D., Brezov, D.S., Mladenov, I.M. (2014). Covariant Decomposition of the Three-Dimensional Rotations. In: Zhang, X., Liu, H., Chen, Z., Wang, N. (eds) Intelligent Robotics and Applications. ICIRA 2014. Lecture Notes in Computer Science(), vol 8918. Springer, Cham. https://doi.org/10.1007/978-3-319-13963-0_51

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  • DOI: https://doi.org/10.1007/978-3-319-13963-0_51

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-13962-3

  • Online ISBN: 978-3-319-13963-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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