jaxtransform3d.rotations.left_jacobian_SO3_inv#

jaxtransform3d.rotations.left_jacobian_SO3_inv(axis_angle: Array) → Array[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:

axis_anglearray-like, shape (…, 3): Compact axis-angle representation.

Returns:

J_invarray, shape (…, 3, 3): Inverse left Jacobian of SO(3).