Rotations / SO(3) group index
Group theory
Ambiguities in rotation representations
Summary
| | Extrinsic/Global | Intrinsic/Local |
|---|
| Active | $\mathbf{x}_2 = T_2 T_1 \mathbf{x}_0$ | $\mathbf{x}_2 = T_1 T_2 \mathbf{x}_0$ |
| Passive | $\mathbf{x}^{\prime\prime} = T_1^{-1}, T_2^{-1} \mathbf{x}$ | $\mathbf{x}^{\prime\prime} = T_2^{-1}, T_1^{-1} \mathbf{x}$ |
- Active $\longleftrightarrow$ passive: invert transformation
- Global $\longleftrightarrow$ local: reverse transformation order
Rotation representations
Orientation parametrisations
Rotation error representation
As Euler angles
Axis/angle
As quaternions
Kinematics
IMU specific
IMU preintegration on manifold
To read