Analytical solutions to the planar atmospheric re-entry equations are derived using the Matched Asymptotic Expansions (MAE) method. In this approach, the exo- and endo-atmospheric flight regimes are considered separately. The aerodynamic coefficients are modelled as affine functions of velocity at hypersonic speeds. A composite solution is obtained by integrating the solutions from each regime together; the adopted matching principle allows this solution to be applied to skip trajectories. The results are compared with those obtained using numerical ODE solvers to validate the accuracy of the solutions obtained and show the improvements over the case with constant aerodynamic coefficients.
Ramirez et al. (Thu,) studied this question.