# New Memorandum "Quaternions and Spatial Rotation" Released

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From M.Eng. René Schwarz, Bremen/Merseburg

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.