## 1 Introduction
In these studies, only simulation purposes are pursued without updating subsystems during optimization, and the focus is on finding the optimum values of a limited set of parameters [28; 29; 30]. On the other hand, while the research on hybrid rockets is expanding with an increasing number of publications, our study distinguishes itself by introducing a novel approach. In a pioneering contribution to the literature, our study introduces an optimization approach by using a 6 DOF model that seamlessly integrates multiple subsystems, including aerodynamic, structural, environmental, propulsion, and trajectory components. This comprehensive integrated framework facilitates the interactive updating of subsystems throughout the optimization study for the first time in the literature. In our study, angular motion (three axes) and linear motion (three axes) are modeled as 6 DOF. Throughout the optimization algorithm, it was observed that the location of the center of gravity, moments of inertia, and aerodynamic forces and moments change depending on the changing length of the launch vehicle after the separation of its stages. In our analysis, the effect of launch vehicle geometry was included in the study since the subsystems work interactively, and optimum results were obtained. In other studies, only linear motion is considered since it is modeled as three degrees of freedom (3 DOF), and only lift and drag are included in aerodynamics [31; 32; 33; 34; 35]. This aerodynamic lift and drag were extracted for the first geometry depending on the Mach number (M), that is, a new database was not created depending on the geometric change in aerodynamic forces. The 3 DOF model stands out for its features of dynamic model simplification, saving on processor power and data processing capacity, and reducing system complexity. On the other hand, the importance of comprehensive modeling that is the closest representation to reality becomes evident in the optimization of subsystems with a dominant impact on the trajectory and performance of the launch vehicle, such as the propulsion system characteristics. However, in our study, we have the chance to examine the moment effects, namely the angular motion, together with other changes. As a different approach from other studies in the literature, an optimum result was successfully achieved while the effects that depend on geometrical changes in aerodynamic forces and the causes of these effects on the trajectory were observed. In this respect, our study looks more comprehensively at the launch vehicle trajectory design problem and, for the first time, the effect of launch vehicle geometry works simultaneously with other parameters in the system, thanks to the interactive subsystems, and a successful optimum result was obtained. In our paper, Section 2 represents the modeling of hybrid launch vehicle subsystems, including aerodynamics, structural, and propulsion factors, as well as environment and gravity models. In Section 3, the main idea behind the optimization problem is defined in detail, along with the provided solution procedure. In Section 4, the comparison results with comprehensive modeling are evaluated. The discussions and conclusions are given in Section 5.