Atmospheric re-entry is a critical aspect of numerous space missions, playing a pivotal role in ensuring the safe landing of crews for human missions and facilitating the return of experiments or samples to Earth. This challenge also holds implications in the military realm, particularly in the context of Intercontinental Ballistic Missiles (ICBMs) and the advanced hypersonic missiles presently under development. This thesis, developed at Thales Alenia Space in Turin, is centred on lifting body re-entry vehicles within Earth's atmosphere from low Earth orbit. There are three primary objectives: firstly, the development of a trajectory optimization tool capable of deriving optimal lifted re-entry trajectories while adhering to mission-specific constraints.