Abstract: To analyze the dynamic stability of hypersonic reentry vehicles along the disturbed trajectory, the linearized longitude dynamics based on small perturbation theory for hypersonic reentry is established in which the gravity grads and the variation of atmospheric density with altitude are both considered. Then the transfer matrix and the characteristic equation are obtained. Based on the results, a longitude mode analysis along the trajectory is carried out. An aerodynamic configuration of a hypersonic reentry vehicle is proposed by using conics and the Class function and Shape function Transformation technique (CST). The aerodynamic characteristic is estimated by the approximate engineering method. A modal stability analysis on typical reentry trajectories is carried out to analyze the maximum range trajectory, minimum range trajectory, and skip trajectory, obtaining the properties of height mode, phugoid mode, and short period mode of hypersonic reentry vehicles. At last, a suggestion for trajectory optimization from the view of longitude dynamic stability is proposed. Despite potential loss of range ability, the design should avoid a large skip in altitude for the designed lifting hypersonic reentry trajectory, because the skip will generate more unstable characteristic roots on short period mode and phugoid mode.

Key words: hypersonic, dynamic, stability, modal, trajectory optimization