Attitude Representations¶
Brahe supports multiple mathematical representations for the attitude, or orientation, of 3D objects such as spacecraft. Each representation has its own advantages and disadvantages depending on the application. These representations are implemented based on the comprehensive treatment found in Representing Attitude: Euler Angles, Unit Quaternions, and Rotation Vectors by James Diebel.
Overview¶
Attitude representation is fundamental to spacecraft dynamics and control. Brahe provides four different representations, each with their own advantages:
- Quaternions: Singularity-free, compact representation (4 parameters)
- Rotation Matrices: Direct transformation matrices (9 parameters)
- Euler Angles: Intuitive angular representation (3 parameters, but with singularities)
- Euler Axis: Axis-angle representation (4 parameters)
Choosing a Representation¶
Use Quaternions when:
- Numerical stability is critical
- Interpolating between attitudes
- Propagating attitude dynamics
Use Rotation Matrices when:
- Transforming vectors between frames
Use Euler Angles when:
- Human readability is important
Use Euler Axis when:
- Representing single rotations about an axis
Conversions¶
All representations can be converted between each other using built-in conversion functions.