2-D solutions in re-entry aerodynamics

We derive integrable solutions for the two-dimensional (2-D) re-entry dynamical equations of motion of a space vehicle, under the assumptions of standard atomospheric model. It is desirable to have analytical solutions for this important and practical problem which arise during the atmospheric re-entry phase. Therefore, 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. By carrying out the closed-form integration, we express the solutions with the Exponential Integra and Generalized Exponential Integral functions. Theoretical frameworks for proposed solutions as well as, several numerical examples, are presented.