New solutions in planar re-entry aerodynamics

In this paper we present integrable solutions for the atmospheric re-entry dynamical equations of motion of a space vehicle, under the assumptions of standard atmospheric model. This is a very important and practical problem encountered during the atmospheric re-entry phase and our solution can be effectively applied to investigate and control the rocket flight characteristics. By setting the initial conditions for the speed, re-entering flight-path angle, altitude, atmosphere density, lift and drag coefficients, the nonlinear differential equations of motion are linearized by a proper choice of the re-entry range angles. After integration, the solutions are expressed with the Exponential Integral, and Generalized Exponential Integral functions. Theoretical frameworks for proposed solutions as well as, several numerical examples, are presented.