Quaternions and Spatial Rotation

  • João Pedro Morais
  • Svetlin Georgiev
  • Wolfgang Sprößig


The particularly rich theory of rotations does not need advertising. One can think of a rotation as a transformation in the plane or in space that describes the position and orientation of a three-dimensional rigid body around a fixed point. The first ever study of rotations was published by L. Euler in 1776.


Rotation Angle Unit Quaternion Quaternion Representation Pure Quaternion Composite Rotation 
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Copyright information

© Springer Basel 2014

Authors and Affiliations

  • João Pedro Morais
    • 1
  • Svetlin Georgiev
    • 2
  • Wolfgang Sprößig
    • 3
  1. 1.CIDMAUniversity of AveiroAveiroPortugal
  2. 2.Department of Differential EquationsUniversity of Sofia St Kliment Ohridski Faculty of Mathematics and InformaticsSofiaBulgaria
  3. 3.Institut für Angewandte AnalysisTU Bergakademie FreibergFreibergGermany

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