## 4 Comparison of the Comprehensive Modeling
Figure 8: The simulation results of the 3 DOF model and 6 DOF model for the original Minotaur-I launch vehicle. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **6 DOF** & **3 DOF** & **Target** &
\begin{tabular}{c} **\% Difference** \\ **(6 DOF/3 DOF)** \\ \end{tabular} \\ \hline \(V\), m/s & 7460.2 & 7587.4 & 7482.2 & 0.29/1.41 \\ \(\gamma\), deg & 0.0052 & 2.665 & 0 & - \\ \(h\), km & 743.7 & 812.4 & 741.2 & 0.34/9.61 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: The comparison summary of 3 DOF and 6 DOF results for the solid last stage. Figure 7: The simulation results of the 3 DOF model and 6 DOF model for the hybrid last stage. accuracy of the results obtained from the 6 DOF simulation is higher compared to that from the 3 DOF simulation. Due to the reasons highlighted in Tables 5 and 6, while the final values obtained through optimization for Design ID 20245 appear similar to the reference values, slight differences are observed at lower stages. Meanwhile, it is observed that the difference between the results of 3 DOF and 6 DOF models is gradually widening. Additionally, it is noticed that the deviation rate of the results obtained with 3 DOF from the target values is also higher. When Table 7 is examined, in the 3 DOF model, complex angular velocity calculations, such as those found in the 6 DOF model, are not present. Additionally, effects like moment of inertia, center of mass, and moment changes are not included, causing the gap between the two models to widen as the simulation progresses. Firstly, when we examine the velocity (\(V\)) parameter, it is observed that the 6 DOF model reaches a speed of 7425 m/s, while the 3 DOF model reaches 6567 m/s. The target speed is set at 7482.2 m/s, and in this case, it is observed that the 6 DOF model deviates by 0.76%, whereas the 3 DOF model deviates by 11.55%. Focusing on another parameter, the flight path angle (\(\gamma\)), the 6 DOF model achieves \(-0.0074\) degrees, while the 3 DOF model reaches 7.2708 degrees. The target angle of attack is set at 0 degrees, and in this situation, it is observed that the 6 DOF model is closer to this target, whereas the 3 DOF model exhibits a significant deviation. Lastly, when we concentrate on the altitude (\(h\)) parameter, the 6 DOF model reaches an altitude of 747.6 km, while the 3 DOF model reaches 807.6 km. The target altitude value is set at 741.2 km, and in this case, it is observed that the 6 DOF model deviates by 0.86%, whereas the 3 DOF model deviates by 8.02%. This analysis provides a detailed insight into the performance differences between the two models. According to Table 8, examining the velocity parameter, we observe that the 6 DOF model achieves a velocity of 7460.2 m/s, while the 3 DOF model reaches 7587.4 m/s. The target \(V\) is set at 7482.2 m/s. In this context, the 6 DOF model exhibits a slight deviation of 0.29%, while the 3 DOF model shows a slightly higher deviation of 1.41%. Shifting the focus to \(\gamma\), we find that the 6 DOF model attains a value of 0.0052 degrees, whereas the 3 DOF model reaches 2.665 degrees. The target flight path angle is specified as 0 degrees. Remarkably, the 6 DOF model aligns closely with this target, demonstrating negligible deviation, while the 3 DOF model shows a notable deviation of 2.665 degrees. Considering the \(h\) parameter, the 6 DOF model reaches an altitude of 743.7 km, while the 3 DOF model achieves 812.4 km. The target altitude is set at 741.2 km. Consequently, the 6 DOF model displays a modest deviation of 0.34%, while the 3 DOF model exhibits a more substantial deviation of 9.61%. While the 6 DOF model closely aligns with the targeted parameters, it is evident that the 3 DOF model results obtained by running with the parameters entered into the 6 DOF model deviate from the targeted parameters. Therefore, it can be concluded that more detailed models like the 6 DOF model provide more accurate results, while 3 DOF models are more suitable for rapid calculations where precise results are not expected.