Closed-form solutions for flight vehicles with high thrust angle

The present work deals with an analytical model for any flight vehicle (e.g., aircraft, rocket, and aerospace plane) with high thrust angle. This work produces closed-form solutions of two (aerodynamic and thrust) nonlinear feedback controls, heat rate, and heat load; and integrates most of the state variables for flight vehicles. The analytical solutions require pairs of equality constant constraints. These include five pairs of equality constant constraints (i.e., constant rate of climb with constant dynamic pressure, constant flight path angle with constant dynamic pressure, constant speed with constant dynamic pressure, constant speed with constant rate of climb, constant acceleration with constant dynamic pressure). The analytical results can be helpful in the general numerical-solutionof the system, where the numerical approach has its classical errors and gives a less general picture than the analytical approach.