## 5 Simulation of Active Detumbling  
In this paper, the Euler angle pose description method was adopted to describe the motion state of space debris. The last stage of the rocket was selected for dynamic modeling of the space debris, providing a dynamic model for the simulation of the subsequent detumbling method. In order to describe the motion status of space debris in orbit, the following assumptions need to be made for space debris:  
1. Space debris is in geosynchronous orbit. When the satellites used for detumbling reach the designated position, the relative position between them can be considered to not change. 2. The space debris is a regular cylinder similar to the last stage of the rocket, with its center is located on the orbital line and the center point not drifting during movement. 3. The rotational inertia of space debris is concentrated on the three main inertia axes and the rotational inertia in other directions is relatively small. 4. The space debris is a rigid body and does not deform during normal operation and detumbling. In active detumbling of space debris, the detumbling satellite observes the target movement through the visual sensor. Then, the surface state of the space debris is analyzed to obtain the topography information of the position where the space debris can be impacted and the target contact area is selected. Finally, the impact position and impact force are calculated by combining the motion state of the space debris and the morphological characteristics of the impactable surface, allowing the final impact posture and impact moment to be determined. Figure 15 shows the execution process of mechanical impact active detumbling. Figure 14: Corrected friction force comparison results. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Experimental Value/N** & 9.18 & 9.2 & 9.25 & 9.58 & 10.7 & 11.1 & 11.4 & 12.1 & 13.1 & 14.3 & 15.5 \\
**Correction Value/N** & 8.91 & 9.18 & 9.42 & 9.67 & 9.97 & 10.4 & 10.8 & 11.6 & 12.6 & 13.8 & 15.2 \\
**Identification Error/\%** & 2.9 & 0.2 & 1.8 & 0.1 & 6.9 & 6.3 & 5.2 & 4.1 & 3.8 & 3.4 & 3.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparative data for the friction force. This simulation used the rocket's last stage as the object of active detumbling, which was approximated as a regular cylinder with three-axis angular momentum and lost attitude adjustment capability. In this simulation experiment, the model had a radius of 1000 mm, a length of 3000 mm, and a mass of 1000 kg. The dynamic model of space debris is shown in Figure 16. The symbols in Figure 16 are defined as follows: \(OXYZ\) is the base coordinate system, \(OX_{L}Y_{L}Z_{L}\) is the angular momentum coordinate system, \(A\) and \(B\) are the center points of the upper and lower end faces of the model, \(P_{1}\) and \(P_{2}\) are the impact positions, \(l\) is the length of the model, and \(r\) is the radius. The \(Y_{L}\) axis of the angular momentum coordinate system in Figure 16 is the direction of the combined angular momentum. The motion state of large space debris was free tumbling motion with a changing nutation angle. The trajectory of the center point A of the space debris end-face in the base coordinate system is shown in Figure 17.  
Figure 16: Dynamic model of space debris. Figure 15: The execution process of mechanical impact active detumbling. Figure 19: Precession angular velocity. Figure 20: Change curve of the nutation angle. Figure 18: Precession angular velocity. Figure 21: Change curve of the nutation angle. The data in Table 5 show that the triaxial angular momentum of the space debris after the impact in Case (1) was attenuated by more than 63%. The data in Table 6 indicate that the angular momentum of the three axes of the space debris after the impact in Case (2) was attenuated by more than 27%. As can be seen from Figures 18 and 19, the precession angular velocity was greatly reduced after impact in both cases.