Editing Gyrocompass (section)

=== First time-dependent rotation ===
Consider another (non-inertial) observer (the 2-O) located at the center of the Earth but rotating about the NS-axis by <math>\Omega.</math> We establish coordinates attached to this observer as
<math display="block">\begin{pmatrix}
X_{2}\\
Y_{2}\\
Z_{2}
\end{pmatrix} = \begin{pmatrix}
\cos\Omega t & \sin\Omega t & 0\\
-\sin\Omega t & \cos\Omega t & 0\\
0 & 0 & 1
\end{pmatrix}\begin{pmatrix}
X_{1}\\
Y_{1}\\
Z_{1}
\end{pmatrix}</math>
so that the unit <math>\hat{X}_{1}</math> versor <math>(X_{1}=1,Y_{1}=0,Z_{1}=0)^{T}</math> is mapped to the point <math>(X_{2} = \cos\Omega t, Y_{2}=-\sin\Omega t, Z_{2}=0)^{T}</math>. For the 2-O neither the Earth nor the barycenter of the gyroscope is moving. The rotation of 2-O relative to 1-O is performed with angular velocity <math>\vec{\Omega}=(0,0,\Omega)^{T}</math>. We suppose that the <math>X_{2}</math> axis denotes points with zero longitude (the prime, or Greenwich, meridian).