Rotation Matrix Exponential

Overview


Rotation Group
{% A = \begin{bmatrix} 0 & - \theta \\ \theta & 0 \\ \end{bmatrix} %}
{% J = \begin{bmatrix} 0 & - 1 \\ 1 & 0 \\ \end{bmatrix} %}
{% e^A = (1 - \frac{\theta^2}{2!} + \frac{\theta^4}{4!} - ... )I_2 + (\frac{\theta}{1!} - \frac{\theta^3}{3!} + ...)J %}
{% e^A = \begin{bmatrix} cos \theta & - sin \theta \\ sin \theta & cos \theta \\ \end{bmatrix} %}