Quaternions are vectors used for computing rotations in mechanics, aerospace, computer graphics, vision processing, and other applications. They consist of four elements: three that extend the commonly known imaginary number and one that defines the magnitude of rotation. Quaternions are commonly denoted as:

`q = w + x*i + y*j + z*k where i² = j² = k² = i*j*k = -1`

This rotation format requires less computation than a rotation matrix.

Common tasks for using quaternion include:

- Converting between quaternions, rotation matrices, and direction cosine matrices
- Performing quaternion math such as norm inverse and rotation
- Simulating premade six degree-of freedom (6DoF) models built with quaternion math

For details, see MATLAB^{®} and Simulink^{®} that enable you to use quaternions without a deep understanding of the mathematics involved.

- Calculating Flight Parameters Using Quaternion Math (Example)
- Quaternion Estimate from Measured Rates in Simulink (Example)
- Astrium Creates Two-Way Laser Optical Link Between an Aircraft and a Communication Satellite (User Story)
- Transforming Coordinate Systems (Example)

- Aerospace Toolbox (Product)
- Aerospace Blockset (Product)
- Flight Parameters and Quaternion Math (Documentation)
- 6DoF (Quaternion) (Documentation)
- Convert Quaternion to Rotation Angles (Function)

*See also*: *Euler angles*, *linearization*, *numerical analysis*, *design optimization*, *real-time simulation*, *Monte Carlo simulation*, *model-based testing*