jaxtransform3d.rotations.left_jacobian_SO3#

jaxtransform3d.rotations.left_jacobian_SO3(axis_angle: Array) → Array[source]#

Left Jacobian of SO(3) at theta (angle of rotation).

\[\frac{\partial Exp(\hat{\boldsymbol{\omega}}\theta)} {\partial\hat{\boldsymbol{\omega}}\theta} = \boldsymbol{J}(\hat{\boldsymbol{\omega}}\theta) = \frac{\sin{\theta}}{\theta} \boldsymbol{I} + \left(\frac{1 - \cos{\theta}}{\theta}\right) \left[\hat{\boldsymbol{\omega}}\right] + \left(1 - \frac{\sin{\theta}}{\theta} \right) \hat{\boldsymbol{\omega}} \hat{\boldsymbol{\omega}}^T\]

Parameters:

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

Returns:

Jarray, shape (…, 3, 3): Left Jacobian of SO(3).