SB blog

When I was searching for uses of quaternions in orientation algorithms, there was always one equation that was shown with no explanation:  $$\begin{array}{}\text{(1)}& \dot{\mathbf{q}}(t)=\frac{1}{2}\mathit{\omega }\mathbf{q}(t)\end{array}$$ but sometimes it was: $$\begin{array}{}\text{(2)}& \dot{\mathbf{q}}(t)=-\frac{1}{2}\mathit{\omega }\mathbf{q}(t)\end{array}$$ or $$\begin{array}{}\text{(3)}& \dot{\mathbf{q}}(t)=-\frac{1}{2}\mathbf{q}(t)\mathit{\omega }\end{array}$$ Moreover, when I was looking for any derivation of these formulas I found out that all resources were several pages - not very encouraging for me or derivations were not complete in their own calculations, which was even more frustrating when you were thinking that finally, you would understand this.  So, I decided to do it myself in 2 ways: first more based on quaternion interpretation and the second old-fashion derivative from the definition. Also, I will discuss frames of reference in which all of the elements are presented. I will provide som...