## 4 Comparison of the Comprehensive Modeling
It can be observed that using 6 DOF models, especially in critical tasks during the design phase, can lead to obtaining more precise results, particularly in satellite launch vehicle projects that require high precision. This, in turn, could potentially shorten the design process, and comprehensive modeling with 6 DOF solutions can yield results closer to reality. In order to elaborate on comprehensive modeling and to observe the difference resulting from comprehensive modeling, 6 DOF results were obtained without a change in the center of gravity, without considering the change in moment of inertia, with constant aerodynamic coefficients, and by combining three scenarios, i.e., without comprehensive modeling. The comparison summaries of comprehensive modeling for the hybrid last stage and solid last stage are presented in Tables 9 and 10, respectively. Table 9 provides a comprehensive comparison of modeling results for the hybrid last stage, considering different scenarios involving variations in center of gravity, moment of inertia, and constant aerodynamics. The table includes results for the 6 DOF model, comparing them to the target values, and showcases the percentage differences for each specific case. Looking at the \(V\) parameter, the 6 DOF model's initial result is 7425 m/s, while the target value is set at 7482.2 m/s. When the model is simulated without a change in center of gravity, the velocity drops to 6603.8 m/s, resulting in an 11.06% deviation from the target. Similarly, without inertia changes, the velocity decreases to 6499.4 m/s, showing a 12.47% deviation. In the case of constant aerodynamics, the velocity further decreases to 6195.5 m/s, with a 16.56% deviation. The combined effect of all three cases results in a significant deviation, with the velocity decreasing to 4613.5 m/s, exhibiting a 37.87% difference from the target orbit velocity. For the \(\gamma\) parameter, the initial 6 DOF result is \(-\)0.0074 degrees, aiming to align with a target of 0 degrees. Without a change in CG, \(\gamma\) increases to 21.8 degrees, deviating from the target. Similarly, without a moment of inertia change, \(\gamma\) becomes \(-\)8.54 degrees, showing a deviation. In the case of constant aerodynamics, \(\gamma\) increases even more to 27.41 degrees, with a substantial deviation. The combined effect of all three cases results in \(\gamma\) of 80.03 degrees, indicating a significant deviation from the target. Examining the \(h\) parameter, the initial 6 DOF result is 747.6 km, with a target set at 741.2 km. Without a change in CG, the altitude increases to 1249.4 km, resulting in a 68.6% deviation from the target. Without inertia changes, the altitude decreases to 896.02 km, showing a 20.9% deviation. In the case of constant aerodynamics, the altitude further increases to 1546.61 km, with a substantial 108.7% deviation. The combined effect of all three cases results in a significant altitude increase to 2417.6 km, exhibiting a 226.2% difference from the target. Table 10 presents results for the 6 DOF model alongside target values and showcases the percentage differences for each specific modeling scenario for the original Minotaur-I launch vehicle (Northrop Grumman, West Falls Church, Virginia). Starting with the \(V\) parameter, the initial 6 DOF result is 7460.2 m/s, with a target value of 7482.2 m/s.