# Multi-Body Dynamics Modeling and Simulation of Maglev Satellites
## 4 Simulation Results and Analysis  
This chapter conducts simulation analysis on the pointing accuracy, pointing stability, dynamic tracking ability, and in-orbit bearing capacity of the Lorentz force magnetic levitation gimbal stabilization platform. It verifies the advantages of payload-centered control methods in improving the accuracy of imaging load control and isolating satellite body vibration, thereby verifying the effectiveness of the proposed high-precision fast attitude pointing control algorithm for imaging loads. The mass parameters of the LFMP are shown in Table 3.  
Set the initial angular velocity of the satellite platform to \(\omega_{b}(0)=\begin{bmatrix}0.001&0&0\end{bmatrix}^{\text{T}}\,\text{rad}/\text{s}\). Set the initial value of imaging load angular velocity to \(\omega_{p}(0)=\begin{bmatrix}0.001&0&0\end{bmatrix}^{\text{T}}\,\text{rad}/\text{s}\). The expected motion of the payload subsystem is to rotate along its own axis while following the \(X\)-axis rotation of the MM at an orbital angular velocity of \(\omega_{0}=0.0011\) rad/s. The reference controller parameters are shown in Table 4 below.  
Conduct attitude control simulation on the LFMP without considering the elastic vibration of the solar wing and the rapid maneuvering of the payload subsystem.  
The axial rotation of the payload subsystem and the control expectation of the MM are shown in Figure 6. The control limit for the position control force of the platform subsystem is set to 0.1 N, the control limit for the payload attitude control torque is set to 0.1 Nm, and the control limit for the payload attitude control force is set to 0.1 N. The control limit for the driving torque of the MM is set to 0.1 Nm.  
According to Figures 7 and 8, the attitude accuracy of the payload subsystem is 0.00002\({}^{\circ}\), and the attitude stability is within 0.00005\({}^{\circ}\)/s.  
According to Figure 9, the position control accuracy is 0.000005 m. According to Figure 10, the driving error of the MM is 0.001\({}^{\circ}\).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Category** & \
\begin{tabular}{c} **Centroid Position/** \\ **Attitude** \\ **Quaternion** \\ \end{tabular} &
\begin{tabular}{c} **Quality** \\ **(kg)** \\ \end{tabular} & \multicolumn{2}{c}{**Moment of Inertia (kg \(\times\) m\({}^{2}\))**} \\ \hline Satellite & \([0,0,-0.4697]\), \([1,0,0,0]\) & 276 & \(\begin{bmatrix}50&0&0\\ 0&60&0\\ 0&0&60\\ \end{bmatrix}\) \\ Payload & \([0,0,0],[1,0,0,0]\) & 15 & \(\begin{bmatrix}1&0&0\\ 0&1&0\\ 0&0&1\\ 0&0&1\end{bmatrix}\) \\ SM & \([0.00538,-0.00781,\\ -0.18687],[1,0,0,0]\) & 26.14 & \(\begin{bmatrix}0.287&7.75\times 10^{-7}&0.016\\ 7.75\times 10^{-7}&0.269&0.029\\ 0.016&0.029&0.41\\ 0.016&1.01\times 10^{-5}&-1.34\times 10^{-5}\\ 1.01\times 10^{-5}&0.029&6.20\times 10^{-7}\\ -1.34\times 10^{-5}&6.20\times 10^{-7}&0.021\\ \end{bmatrix}\) \\ PM & \([0,0,0],[1,0,0,0]\) & 1.7599 & \(\begin{bmatrix}0.0021&8.48\times 10^{-11}&-6.46\times 10^{-10}\\ 8.48\times 10^{-11}&0.0019&-2.79\times 10^{-7}\\ -6.46\times 10^{-10}&-2.79\times 10^{-7}&0.0037\end{bmatrix}\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: LFMP Parameters.  
Figure 6: Control expectations. (**a**) Expected angle; (**b**) expected angular velocity; (**c**) expected angular acceleration.  
Figure 8: Attitude stability of payload subsystem.  
Figure 7: Attitude accuracy of payload subsystem.  
Figure 9: Platform subsystem position control accuracy.  
It can be seen that in the payload-centered control method, the payload subsystem has higher accuracy and smoother motion compared to the platform subsystem. This verifies the advantage of the payload-centered control algorithm in improving the accuracy of payload imaging control, and further verifies the effectiveness of the high-precision fast attitude pointing control algorithm for imaging payloads.