## 6 Discussion  
The measurement system deviations for determining the mass characteristics of the pico-satellite can be caused by several reasons. First, there are deviations between the 3D design, actual machining, and assembly of the measurement system. Second, there are deviations between the 3D design, actual machining, and assembly of the standard workpiece, work fixture, and pico-satellite that can affect the position of the centroid and moment of inertia. Third, the weighing and angular velocity sensors have a certain measurement deviation, which can lead to deviation in the centroid and moment of inertia. Moreover, the measurement system has friction resistance and air resistance, and the torque of the motor has periodic deviation, which could lead to the deviation of the angular velocity. Additionally, the horizontal tilt of the system can also lead to deviations of the centroid and moment of inertia.  
The measurement system has application limits, and the motor torque parameters, weighing sensor parameters, experimental safety, and accuracy should be considered when determining these application limits. The weight range of the measurement object is 10-50 kg; the deviation range of the centroid is 0-250 mm; and the range of the moment of inertia is 0.08-1 kgm\({}^{2}\). The measurement time of the centroid is less than 15 min, and the measurement time of the moment of inertia is less than 20 min, which is a small amount of time when considering the applicability of the measurement system. In addition, the deviation of the centroid and moment of inertia is less than 2.5 mm, 1.5 mm, 20 kgm\({}^{2}\), and 0.6 kgm\({}^{2}\) in the literature [9; 15], respectively, and their accuracy of measurement is inferior to our measurement system. The cost of the measurement system is approximately $50,000 in the literature [25], and the assembly and test process are complicated and time consuming. Hence the mass characteristic measurement system developed herein has many benefits, such as its low cost (approximately $3000), simple processing and assembly, and easy operation.  
Figure 14: **(a)** The relationship between angular velocity and time in different states; (b) the partial enlarged detail in the dash dot frame.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \(t=0.5\) s & **Vertical** & **Horizontal** & **Horizontal** & **Center of Mass Moment** & **Center of Mass Theory** & **Deviations (kgm\({}^{2}\))** \\  & **Position** & **Position** & **Position** & **Position** & **of Inertia (kgm\({}^{2}\))** & **Moment of Inertia (kgm\({}^{2}\))** \\ \hline \(\omega_{2}\) (\({}^{\circ}\)/s) & 71.706 & 33.902 & 33.658 & \(J_{LG}=2.817\times 10^{-1}\) & \(J_{LG}=2.8\times 10^{-1}\) & \(\Delta J_{LG}=1.7\times 10^{-3}\) \\ \(\omega_{3}\) (\({}^{\circ}\)/s) & 56.849 & 25.922 & 25.727 & \(J_{LG}=5.841\times 10^{-1}\) & \(J_{LG}=5.692\times 10^{-1}\) & \(\Delta J_{LG}=1.49\times 10^{-2}\) \\ \(J_{LG}\) (kgm\({}^{2}\)) & 2.841 \(\times 10^{-1}\) & 7.373 \(\times 10^{-1}\) & 7.383 \(\times 10^{-1}\) & \(J_{LG}=5.861\times 10^{-1}\) & \(J_{LG}=5.724\times 10^{-1}\) & \(\Delta J_{LG}=1.37\times 10^{-2}\) \\ \hline \end{tabular}
\end{table}
Table 14: The comparison of moment of inertia between experimental and theoretical results.