Approximate analytical analysis for phugoid characteristic of reentry vehicles and its applications

For the hypersonic reentry vehicle adopting the equilibrium glide-based numerical or analytical predictor-corrector guidance, the phugoid oscillation of the reentry trajectory is prone to be caused at the transition point from the initial descent to the equilibrium glide or by large prediction deviations. With the increase of the lift-to-drag ratio of reentry vehicles under research in recent years, the phugoid oscillation becomes more noticeable to cause researchers to re-examine the hypersonic phugoid characteristic. A concise approximate analytical solution for intuitively expressing the dominate factors for hypersonic phugoid characteristic of reentry vehicles is derived, according to three order longitudinal flight dynamics equations and the equilibrium glide condition. It is found that the hypersonic phugoid damping characteristic mainly depends on the ratio of flight speed to orbital speed and the phugoid correction factor, rather than on the atmospheric density-gradient parameter considered by previous researchers. A controller is designed to eliminate the trajectory oscillation by using the approximate relation derived, further improving the equilibrium glide based numerical or analytical predictor-corrector guidance. Effectiveness of the method is verified by the simulation results.