Long-period oscillations of aircraft at hypersonic speeds

Dan theoretical analysis long periodic (fugoid) oscillations of an aircraft having a lifting force and committing flight of hypersonic speed in free atmosphere. The reason of the fluctuations is the mutual transition of the kinetic energy into potential in flight trajectory, which has really determined primarily adjustable longitudinal moment equal to zero at the established flight. It is shown that with the approach of the velocity of the first space reducing the force of gravity height prevails over the reduction of density of the atmosphere so that with the growth rate of the period fugoids fluctuations asymptotically tends to the corresponding period of this satellite. Analytical expressions are obtained for short-period fluctuations, or fluctuations on the angle of attack. It is shown that both these expressions and the expression for long periodic fluctuations in good agreement with the results of the numerical solution.