Thrust law effects on the longitudinal stability of hypersonic cruise

In the present analytical treatment of the cruising flight stability of an aerospacecraft in nearly circular orbit, on the basis of a thrust law which arbitrarily depends on altitude, speed, and angle of attack, attention is given to thrust law effects on the translational (height and phugoid) and rotational (angle of attack) modes. The partial derivatives of the propulsive forces in conjunction with the aerodynamic forces, with respect to speed and altitude, are noted to exert a major influence on the stability of translational dynamics; the partial derivative of the component of propulsive and aerodynamic forces which is perpendicular to vehicle velocity (with respect to the angle of attack) is a primary determinant of the damping of angle-of-attack oscillations, while the partial derivative of the sum about the center of mass of aerodynamic and propulsive pitching moments, with respect to the angle of attack, determines the corresponding period.