The article presents the theoretical analysis of the long-period (phugoid) aircraft oscillations, which has a lifting force and performs a flight at hypersonic speeds in any atmosphere. Oscillations are caused by mutual transition of kinetic energy into potential energy during the flight along the path having an oscillatory character and being determined primarily by controlled longitudinal zero momentum in steady flight. The study shows that with the speed approximating to the first cosmic speed, the decrease in gravity at height dominates the decrease in density of the atmosphere, so that with increasing speed the period of phugoid oscillations tends asymptotically to the corresponding period of the satellite. During the research there were obtained analytical expressions for the short-period oscillations or vibrations at the angle of attack. The study demonstrates that these expressions, as well as the expressions for the long-period oscillations are in good agreement with numerical solutions.
Sidnyaev N., Glushkov P. Long-period oscillations of aircraft at hypersonic speeds. Маthematical Modeling and Coтputational Methods, 2014, №1 (1), pp. 99-114