Re-entry dynamics of the reusable stage of a space launcher: a first level model

The development of reusable launchers has increased significantly in recent years, mainly due to the advent of private companies that have achieved great successes in this field. The main reasons for going down this path are to reduce the cost and environmental impact of the space industry. This paper addresses the study of the re-entry dynamics and control of the first stage of a reusable launcher schematized as a rigid body having 3 DOF, the translations in the vertical plane and the rotation in pitching. The re-entry dynamics is faced by solving nonlinear-coupled differential equations. The study begins with the flip maneuver that takes place above the Kàrmàn line and finishes with the stage landing. Stability in the dense atmosphere is studied through a state space model at different altitudes. Results include the time histories of descent velocity, attitude and altitude, obtained through the implementation of an in-house code, as well as the mathematical expressions of the transfer functions of the system in the state space related to the last part of the re-entry maneuver. This latter result is the most important as it makes the model general and allows the study of a number of cases of interest as the system inputs change.