Closed-form control and state solutions for flight with equality constraints

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