## 5 Discussion  
According to Table 5, the conclusions are as follows:  
1. The maximum error of the typical response frequency value has a relatively small value of 0.39%. It proves that the proposed integrated modeling method can accurately capture the typical characteristic response of flywheel micro-vibration disturbance, and it has important reference significance for satellite micro-vibration isolation design.  
2. Figure 16 shows the time-domain data of simulation results and experimental results of image shift in the Y-direction. It is shown that the results are close to the same magnitude in the time-domain. The RMS of the simulation results is 0.4391 pixels, and the RMS of the experimental results is 0.3275 pixels, with an error of 34.08%. According to the results of [PERSON] et al. from modeling and analysis of Solar Dynamics Observatory (SDO) micro-vibration, the RMS predicted by the simulation results is usually 1.5-2 times that of  
Figure 15: Frequency-domain response of simulation and experiment.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{2}{c}{**RMS**} \\ \hline \multicolumn{3}{c}{**Simulation Results (Pixel)**} & \multicolumn{2}{c}{**Experimental Results (Pixel)**} & **Errors** \\ \hline  & 0.4391 & 0.3275 & 34.08\% \\ \hline  & \multicolumn{2}{c}{**Frequency**} \\ \hline  & **Simulation Results (Hz)** & **Experimental Results (Hz)** & **Errors** \\ \hline response 1 & 127.7 & 128.2 & 0.39\% \\ response 2 & 197.3 & 197.8 & 0.25\% \\ response 3 & 255.9 & 256.7 & 0.31\% \\ response 4 & 394.5 & 395.5 & 0.25\% \\ response 5 & 493.2 & 494.4 & 0.24\% \\ \hline  & \multicolumn{2}{c}{**Amplitude**} \\ \hline  & **Simulation Results (Pixel)** & **Experimental Results (Pixel)** & **Errors** \\ \hline response 1 & 0.022 & 0.013 & \(-\)69.23\% \\ response 2 & 0.052 & 0.058 & 10.34\% \\ response 3 & 0.014 & 0.017 & 17.64\% \\ response 4 & 0.028 & 0.065 & 56.92\% \\ response 5 & 0.017 & 0.028 & 39.29\% \\ \hline \hline \end{tabular}
\end{table}
Table 5: Comparison of RMS and amplitude/frequency at typical response.  
the experimental results [27]. The error of RMS in this paper is 1.34 times, which is within a reasonable range.  
3. The amplitude results of typical responses are relatively different in terms of errors range, due to/stemming from errors inherited in experimental results and inaccurate mode damping values. The transfer function derived from the Laplace transform of the dynamic differential Equation (4) is as follows  
\[H_{ij}(\omega)=\sum_{r=1}^{N}\frac{\phi_{ri}\phi_{rj}}{m_{r}[(\omega_{r}^{2}- \omega^{2})+j2\xi_{r}\omega_{r}\omega]} \tag{9}\]  
where the value of mode damping \(\xi_{r}\) of each mode determines the response amplitude. Although the relevant mode damping has not been precisely adjusted, the accuracy of RMS analysis results is still better than that of previous research results. After the mode damping is adjusted, an analysis error can be further reduced, and analysis accuracy can be further improved.  
4. In the finite element simulation, we found that typical modes of sensitive optics in satellites include the response of the secondary mirror at 127, 394, and 493 Hz and the response of the primary mirror at 197, 256, and 320 Hz. From the simulation results (Figure 4), due to the micro-vibration disturbance of the flywheel, the satellite natural modes are excited at 127, 197, 256, 394, and 493 Hz. However, since there is no disturbance input near 320 Hz, the natural mode of the main mirror does not respond at 320 Hz, so there is no peak at 320 Hz in the frequency domain results of the imaging pixels. In addition, there are some inherent modes with small amplitude (less than 0.01 pixel) in Figure 10, whose magnitude is at the same magnitude as the experimental environment noise, and will not have a significant impact on satellite imaging.