Infinitesimal Rotations

The compact definition $\mathbf{w}=\vartheta \mathbf{k}$ combined with Rodrigues' formula allows for the expression of infinitesimal rotations in a manner that is very straightforward to compute.

If we send $\vartheta$ to infinitesimals, the formula (A.12) can be approximated as

$$\mathbf{R} \approx \mathbf{I} + \sin \vartheta [\mathbf{k}]_... ...& w_y \\ w_z & 1 & -w_z \\ -w_y & w_z & 1 \\ \end{bmatrix}$$ (A.16)