## 5 Discussions, Conclusions, and Future Work
### Nomenclature
\begin{tabular}{l l} \(\Delta\theta\) & System accuracy; Root mean square (RMS) of the angular deviation between the ideal and the real pointing positions \\ \(\mathrm{t_{s}}\), \(\mathrm{T_{s}}\), \(\mathrm{n_{s}}\) & Total sampling time in \([\mathrm{s}]\), sampling period in \([\mathrm{s}]\), sampling number of system accuracy \\ \(\Delta\overline{\theta}\) & Mean of sampling values \\ \(\Delta\theta_{\mathrm{si}}\), \(\Delta\theta_{\mathrm{syi}}\), \(\Delta\theta_{\mathrm{syi}}\) & Sample value of the ith sample and its components along the y and z-axes of the inertial coordinate \\ \(\sigma_{\Delta\theta}\) & Standard error of sample values \\ \(\overset{\rightarrow}{\mathrm{V_{ib}}}\), \(\mathrm{v_{ibx}}\), \(\mathrm{v_{iby}}\), \(\mathrm{v_{ibz}}\) & Linear velocity vector of the system base in the inertial coordinated and its components along the three axes of the coordinate in \([\mathrm{m/s}]\) \\ \(\overset{\rightarrow}{\mathrm{\omega_{ib}}}\), \(\mathrm{\omega_{ibx}}\), \(\mathrm{\omega_{iby}}\), \(\mathrm{\omega_{ibz}}\) & Angular velocity vector of the system base in the inertial coordinated and its components around the three axes of the coordinate in \([\mathrm{rad/s}]\) \\ \(\overset{\rightarrow}{\mathrm{\omega_{ia}}}\), \(\mathrm{\omega_{iax}}\), \(\mathrm{\omega_{iay}}\), \(\mathrm{\omega_{iaz}}\) & Angular velocity vector of the azimuth in the inertial coordinate and its components around the three axes of the coordinate in \([\mathrm{rad/s}]\) \\ \(\theta_{\mathrm{a}}\), \(\hat{\theta}_{\mathrm{a}}\) & Rotation angle in \([\mathrm{rad}]\) and angular velocity in \([\mathrm{rad/s}]\) of azimuth compensation \\ \(\overset{\rightarrow}{\mathrm{\omega_{ip}}}\), \(\omega_{\mathrm{ipx}}\), \(\omega_{\mathrm{ipy}}\), \(\omega_{\mathrm{ipz}}\) & Angular velocity vector of the pitch in the inertial coordinate and its components around the three axes of the coordinate in \([\mathrm{rad/s}]\) \\ \(\theta_{\mathrm{p}}\), \(\hat{\theta}_{\mathrm{p}}\) & Rotation angle in \([\mathrm{rad}]\) and angular velocity in \([\mathrm{rad/s}]\) of pitch compensation \\ \(\mathrm{R_{b}^{a}}\) & Rotation transformation matrix from the system base coordinate to that of the azimuth \\ \(\overset{\rightarrow}{\mathrm{R_{b}^{p}}}\) & Rotation transformation matrix from the azimuth coordinate to that of the pitch \\ \(\overset{\rightarrow}{\mathrm{\omega_{ba}}}\) & Angular velocity vector of the azimuth in the system base coordinate in \([\mathrm{rad/s}]\) \\ \(\overset{\rightarrow}{\mathrm{\omega_{ap}}}\) & Angular velocity vector of the pitch in the azimuth coordinate in \([\mathrm{rad/s}]\) \\ \(\overset{\rightarrow}{\mathrm{\omega_{ip}}}\), \(\mathrm{\omega_{ibx}^{p}}\), \(\mathrm{\omega_{iby}^{p}}\), \(\mathrm{\omega_{ibz}^{p}}\) & Projection of the system base angular velocity and its components, relative to the inertia coordinate in \([\mathrm{rad/s}]\) \\ \(\overset{\rightarrow}{\mathrm{\omega_{bp}^{p}}}\), \(\mathrm{\omega_{bpx}^{p}}\), \(\mathrm{\omega_{bpy}^{p}}\), \(\mathrm{\omega_{bpz}^{p}}\) & Projection of the pitch angular velocity relative to the system base in the pitch coordinate in \([\mathrm{rad/s}]\) \\ \(\mathrm{\omega_{gyro}}\), \(\mathrm{\omega_{gyro}}\), \(\mathrm{\omega_{gyro}}\) & Sensitive velocities of the azimuth and pitch gyroscopes in \([\mathrm{rad/s}]\) \\ \(\mathrm{U_{m}}\) & Motor armature voltage in \([\mathrm{v}]\) \\ \(\mathrm{I_{m}}\) & Armature current in \([\mathrm{A}]\) \\ \(\mathrm{R_{m}}\) & Total resistor of the armature circuit in \([\mathrm{\Omega}]\) \\ \(\mathrm{L_{m}}\) & Total inductance of the armature circuit in \([\mathrm{H}]\) \\ \(\mathrm{J_{ma}}\) & Rotary inertia of the azimuth motor in \([\mathrm{kg}\):\(\mathrm{m^{2}}]\) \\ \(\mathrm{J_{La}}\) & Rotary inertia of the azimuth load in \([\mathrm{kg}\):\(\mathrm{m^{2}}]\) \\ \(\mathrm{J_{mp}}\) & Rotary inertia of the pitch motor in \([\mathrm{kg}\):\(\mathrm{m^{2}}]\) \\ \(\mathrm{J_{LP}}\) & Rotary inertia of the pitch load in \([\mathrm{kg}\):\(\mathrm{m^{2}}]\) \\ \(\mathrm{D_{L}}\) & Damping coefficient of the two motors \\ \(\mathrm{K_{L}}\) & Elastic coefficient of the two motors \\ \(\mathrm{\theta_{m}}\) & Output angle of the motor side in \([\mathrm{rad}]\) \\ \(\mathrm{\theta_{L}}\) & Output angle of the load side in \([\mathrm{rad}]\) \\ \(\mathrm{E_{m}}\) & Back electro-dynamic force (EMF) of the armature circuit in \([\mathrm{v}]\) \\ \(\mathrm{C_{e}}\) & EMF coefficient of the two motors \\ \(\mathrm{C_{m}}\) & Motor torque coefficient of the two motors \\ \(\mathrm{U_{c}}\) & Control voltage of the motor armature in \([\mathrm{v}]\) \\ \(\mathrm{K_{p}}\) & Amplification coefficient of the driving circuit \\ \(\mathrm{T_{p}}\) & lagging time of the motor armature in \([\mathrm{s}]\) \\ \(\mathrm{E_{s}}\) & EMF of the driving circuit in \([\mathrm{v}]\) \\ \(\mathrm{R_{s}}\) & Resistor of the driving circuit in \([\mathrm{\Omega}]\) \\ \end{tabular}