This thesis presents the development of an open-loop optimization framework for computing the optimal ascent trajectory of a multi-stage booster, with specific application to the insertion of a Hypersonic Glide Vehicle (HGV) into its glide phase. The study addresses the challenge of guiding a launch vehicle through atmospheric and exo-atmospheric regimes while satisfying physical and terminal constraints. The HGV insertion case provides a relevant example, given the growing interest in boost-glide systems for both defense and research applications.

The optimization problem is formulated using the Pontryagin Maximum Principle (PMP), enabling an indirect method that solves the coupled state--costate dynamics with strict boundary conditions. The ascent is modeled as a 3-DoF point-mass in Cartesian coordinates, taking into account aerodynamic forces, Earth's rotation, and path-and-control constraints. This study presents a suitable constraint set and problem definition for the optimization problem that improves numerical convergence. A multiple-shooting approach is used to ensure convergence for the nonlinear dynamics, while a homotopy continuation strategy gradually incorporates aerodynamic and path constraints to improve numerical robustness. Furthermore, the developed trajectory optimization model allows for the implementation of arbitrary boosters that include staging and throttle management.

Results demonstrate smooth, dynamically consistent ascent trajectories that meet target insertion conditions required for an efficient HGV glide. In addition, this report introduces various evaluation techniques for the computed trajectories, together with verification methods that ensure their physical accuracy. Overall, the work delivers a comprehensive and extensible framework for optimal ascent guidance under realistic aerodynamic and operational constraints, with direct applicability to modern boost-glide mission design.