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).
\[\boldsymbol{J}^{-1}(\theta) = \frac{\theta}{2 \tan{\frac{\theta}{2}}} \boldsymbol{I} - \frac{\theta}{2} \left[\hat{\boldsymbol{\omega}}\right] + \left(1 - \frac{\theta}{2 \tan{\frac{\theta}{2}}}\right) \hat{\boldsymbol{\omega}} \hat{\boldsymbol{\omega}}^T\]- 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.