Covariant Decomposition of the Three-Dimensional Rotations

  • Clementina D. Mladenova
  • Danail S. Brezov
  • Ivaïlo M. Mladenov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8918)


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.


Rotations vector-parameterization group decompositions Lie algebras Lie groups 


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Clementina D. Mladenova
    • 1
  • Danail S. Brezov
    • 2
  • Ivaïlo M. Mladenov
    • 3
  1. 1.Institute of MechanicsBulgarian Academy of SciencesSofiaBulgaria
  2. 2.Civil Engineering and GeodesyUniversity of ArchitectureSofiaBulgaria
  3. 3.Institute of BiophysicsBulgarian Academy of SciencesSofiaBulgaria

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