Quaternion

Apply rotation in three dimensional space through complex vectors

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.

MATLAB^® and Simulink^® make it easy to use quaternions without a deep understanding of the mathematics involved. MATLAB and Simulink enable you to:

• Convert between quaternions, rotation matrices, and direction cosine matrices
• Perform quaternion math such as norm inverse and rotation
• Simulate premade six degree-of freedom (6DoF) models built with quaternion math

Examples

• 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)

Software Reference

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

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