\overrightarrow{OS}|_{\mathcal{R}_H}=\mathcal{N}^{-1}\cdot\mathcal{M}^{-1}\cdot\overrightarrow{OS}|_{\mathcal{R}_{SH}}=\left\lbrack \begin{array}{ccc} \cos H & -\sin H & 0 \\ \sin H & \cos H & 0 \\ 0 & 0 & 1 \end{array} \right\rbrack \cdot \left\lbrack \begin{array}{ccc}\cos  \delta & 0 & -\sin \delta \\ 0 & 1 & 0 \\ \sin \delta & 0 & \cos \delta \end{array}\right \rbrack \cdot \left(\begin{array}{c}1 \\ 0 \\ 0 \end{array}\right)=\left(\begin{array}{c}\cos H \cos \delta \\ \sin H \cos \delta \\ \sin \delta \end{array}\right).