pytransform3d.rotations.left_jacobian_SO3_inv¶
- pytransform3d.rotations.left_jacobian_SO3_inv(omega)[source]¶
Inverse left Jacobian of SO(3) at theta (angle of rotation).
![\boldsymbol{J}^{-1}(\theta)
=
\frac{\theta}{2 \tan{\frac{\theta}{2}}} \boldsymbol{I}
- \frac{\theta}{2} \left[\hat{\boldsymbol{\omega}}\right]
+ \left(1 - \frac{\theta}{2 \tan{\frac{\theta}{2}}}\right)
\hat{\boldsymbol{\omega}} \hat{\boldsymbol{\omega}}^T](../_images/math/040e1aff54bb17cb9498ea61c06e708ae36ca51b.png)
- Parameters:
- omegaarray-like, shape (3,)
Compact axis-angle representation.
- Returns:
- J_invarray, shape (3, 3)
Inverse left Jacobian of SO(3).
See also
left_jacobian_SO3Left Jacobian of SO(3) at theta (angle of rotation).
left_jacobian_SO3_inv_seriesInverse left Jacobian of SO(3) at theta from Taylor series.