Optimisation Problem of Entry into Earth's Atmosphere

A study has been carried out on the variation of velocity, time, re-entry angle and distance along the horizontal with altitude for a re-entry vehicle diving into the earth's atmosphere, using the improved version of Marinescu's model that accounts for gravity and assuming that the distance along the earth's surface is fixed. More specifically, after formulating the problem as an isoperimetric one, its Euler-Lagrange equation, which turned out to be a highly nonlinear differential equation of the second order, has been solved via Runge-Kutta method and Simpson's rule for some physically realisable values of the parameters involved