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New Memorandum "Quaternions and Spatial Rotation" Released

From M.Eng. René Schwarz, Bremen/Merseburg
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Preview of Memorandum #6: Quaternions and Spatial Rotation

The Memorandum "Quaternions and Spatial Rotation" has been published as part of my Memorandum Series. It provides a compact introduction into quaternions and their application for spatial rotations:

  • brief introduction into quaternions, their components, notations, and properties
  • quaternion algebra formulary summarizing
    • basic properties (quaternion equality, hypercomplex conjugate, norm, and inverse)
    • basic operations (quaternion addition and subtraction, multiplication, division, normalization, cross and dot product)
    • exponential and logarithmic functions (quaternion exponential function, natural logarithm, logarithmic functions, power and root functions)
    • trigonometric and hyperbolic functions of quaternions
  • application of quaternions in the context of spatial rotations, quaternion rotation operators, rotations and transformations
  • conversion algorithms:
    • Euler Angles to Quaternion (for all 12 possible rotation sequences)
    • Quaternion to Euler Angles (for all 12 possible rotation sequences)
    • Direction Cosine Matrix (DCM) to Quaternion
    • Quaternion to Direction Cosine Matrix (DCM)
    • Euler Angles to Rotation Matrix (for all 12 possible rotation sequences)
  • time derivative of a rotation quaternion
  • quaternion interpolation algorithms
    • linear interpolation (LERP)
    • spherical linear interpolation (SLERP)

Have a look here if you are also interested into other Memoranda out of my Memorandum Series.