pytransform3d.rotations.left_jacobian_SO3¶
- pytransform3d.rotations.left_jacobian_SO3(omega)[source]¶
Left Jacobian of SO(3) at theta (angle of rotation).
![\boldsymbol{J}(\theta)
=
\frac{\sin{\theta}}{\theta} \boldsymbol{I}
+ \left(\frac{1 - \cos{\theta}}{\theta}\right)
\left[\hat{\boldsymbol{\omega}}\right]
+ \left(1 - \frac{\sin{\theta}}{\theta} \right)
\hat{\boldsymbol{\omega}} \hat{\boldsymbol{\omega}}^T](../_images/math/16f028b1005ff667315ad7a7688d6eb87bbe6a8d.png)
- Parameters:
- omegaarray-like, shape (3,)
Compact axis-angle representation.
- Returns:
- Jarray, shape (3, 3)
Left Jacobian of SO(3).
See also
left_jacobian_SO3_seriesLeft Jacobian of SO(3) at theta from Taylor series.
left_jacobian_SO3_invInverse left Jacobian of SO(3) at theta (angle of rotation).