## 4 Comparison of the Comprehensive Modeling
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & & \multicolumn{4}{c}{**Without CG Change**} & \multicolumn{2}{c}{**Without Inertia Change**} \\  & **6 DOF** & **Target** & **Results** & **\% Difference** & **Results** & **\% Difference** \\ \hline \(V\), m/s & 7460.2 & 7482.2 & 6690.4 & 10.6 & 6301.3 & 15.8 \\ \(\gamma\), deg & 0.0052 & 0 & 16.5 & - & \(-\)6.9 & - \\ \(h\), km & 743.7 & 741.2 & 1102.6 & 48.8 & 913.4 & 23.2 \\ \hline  & & \multicolumn{4}{c}{**Constant Aero**} & \multicolumn{2}{c}{**Combined 3 Cases**} \\  & **6 DOF** & **Target** & **Results** & **\% Difference** & **Results** & **\% Difference** \\ \hline \(V\), m/s & 7460.2 & 7482.2 & 6023.4 & 19.5 & 4209.2 & 43.7 \\ \(\gamma\), deg & 0.0052 & 0 & 31.8 & - & 77.1 & - \\ \(h\), km & 743.7 & 741.2 & 1325.9 & 78.9 & 2269.3 & 206.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: The comparison summary of comprehensive modeling results for the original Minotaur-I launch vehicle. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & & \multicolumn{4}{c}{**Without CG Change**} & \multicolumn{2}{c}{**Without Inertia Change**} \\  & **6 DOF** & **Target** & **Results** & **\% Difference** & **Results** & **\% Difference** \\ \hline \(V\), m/s & 7425 & 7482.2 & 6603.8 & 11.06 & 6499.4 & 12.47 \\ \(\gamma\), deg & \(-\)0.0074 & 0 & 21.8 & - & \(-\)8.54 & - \\ \(h\), km & 747.6 & 741.2 & 1249.4 & 68.6 & 896.02 & 20.9 When simulating without a change in CG, the velocity decreases to 6690.4 m/s, resulting in a 10.6% deviation from the target. Without a moment of inertia change, the velocity further decreases to 6301.3 m/s, showing a 15.8% deviation. In the case of constant aerodynamics, the velocity decreases even more to 6023.4 m/s, with a 19.5% deviation. The combined effect of all three cases results in a substantial drop in velocity to 4209.2 m/s, exhibiting a significant 43.7% difference from the target. For the \(\gamma\) parameter, the initial 6 DOF result is 0.0052 degrees, aiming to align with a target of 0 degrees. Without a change in CG, \(\gamma\) increases to 16.5 degrees, deviating from the target value. Similarly, without a moment of inertia changes, \(\gamma\) becomes \(-6.9\) degrees, showing a deviation. In the case of constant aerodynamics, \(\gamma\) increases even more to 31.8 degrees, with a substantial deviation. The combined effect of all three cases results in \(\gamma\) of 77.1 degrees, indicating a significant deviation from the target. Examining the \(h\) parameter, the initial 6 DOF result is 743.7 km, with a target set at 741.2 km. Without a change in CG, the altitude increases to 1102.6 km, resulting in a 48.8% deviation from the target. Without a moment of inertia changes, the altitude decreases to 913.4 km, showing a 23.2% deviation. In the case of constant aerodynamics, the altitude further increases to 1325.9 km, with a substantial 78.9% deviation. The combined effect of all three cases results in a significant altitude increase to 2269.3 km, exhibiting a substantial 206.2% difference from the target. This detailed analysis highlights the diverse impacts of CG, moment inertia, and aerodynamic changes on the comprehensive modeling results. Therefore, it can be observed that comprehensive modeling leads to a critical difference in the optimization process, while in simulations without comprehensive modeling, the desired trajectory is achieved using different design parameters. For example, it is known that the flight path angle plays a dominant role in the trajectory of the launch vehicle, and the flight path angle is directed by the TVC angle. In this study, for instance, while the TVC angle of the first stage is sufficient for placing the payload on the target orbit in the 6 DOF model when it is 4.882 degrees, in the 3 DOF model, a different value from 4.882 degrees could be used to place the payload on the target orbit.