pytransform3d.rotations.left_jacobian_SO3#
- pytransform3d.rotations.left_jacobian_SO3(omega)[source]#
Left Jacobian of SO(3) at theta (angle of rotation).
\[\boldsymbol{J}(\theta) = \frac{\sin{\theta}}{\theta} \boldsymbol{I} + \left(\frac{1 - \cos{\theta}}{\theta}\right) \left[\hat{\boldsymbol{\omega}}\right] + \left(1 - \frac{\sin{\theta}}{\theta} \right) \hat{\boldsymbol{\omega}} \hat{\boldsymbol{\omega}}^T\]- 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).