A nonlinear, physics-based model of the longitudinal dynamics for an air-breathing hypersonic vehicle is developed. The model is derived from first principles and captures a number of complex interactions between the propulsion system, aerodynamics, and structural dynamics. Unlike conventional aircraft, air-breathing hypersonic vehicles require that the propulsion system be highly integrated into the airframe. Furthermore, full-scale hypersonic aircraft tend to have very lightweight, flexible structures that have low natural frequencies. Therefore, the first bending mode of the fuselage is important, as its,deflection affects the amount of airflow entering the engine, thus influencing the performance of the propulsion system. The equations of motion for the flexible aircraft are derived using Lagrange's equations. The equations of motion capture inertial coupling effects between the pitch and normal accelerations of the aircraft and the structural dynamics. The linearized aircraft dynamics are found to be unstable and, in most cases, exhibit nonminimum phase behavior. The linearized model also indicates that there is an aeroelastic mode that has a natural frequency more than twice the frequency of the fuselage bending mode, and the short-period mode is very strongly coupled with the bending mode of the fuselage.
