New Memorandum "Quaternions and Spatial Rotation" Released

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.