Using the Method of Matched Asymptotic Expansions, Analytically Investigate the Three-Dimensional, Atmosphere Entry Problem

Although numerical techniques exist to obtain solutions to highly nonlinear and highly coupled systems, the trends and subtleties of the solution are frequently lost in the volume and form of tabular and graphical data in covering a wide range of initial conditions. This study presents and analytical investigation of the three-dimensional equations of motion for lifting entry into a planetary atmosphere. In this study, the equations of motion for lifting entry into a planetary atmosphere are derived. A non-rotating, spherical planet is assumed, as is a non-rotating, strictly exponential atmospheric model. The derived equations of motion are transformed to a variable set relating the classical orbital elements to the vehicles altitude. Solutions to the resulting five nonlinear, coupled, first order, ordinary differential equations are obtained by using the Method of Matched Asymptotic Expansions and a computerized symbolic manipulator, which performs the detailed algebraic computations. By using the planetary scale height-mean equatorial radius PSHMER product as a small parameter, both zero and first order expansions to the equations of motion are obtained. Keywords Lifting reentry, Reentry trajectory, Orbital mechanics, Planetary entry, Entry dynamics, Theses.