为研究高超声速再入飞行器沿弹道的自由扰动运动的稳定性，考虑大气密度随高度的变化和引力梯度，建立了高超声速无动力再入纵向动力学小扰动线性化方程，然后获得转移矩阵和特征方程，在此基础上进行沿弹道的纵向模态分析。利用二次曲线及基于类型函数和形状函数（CST）的方法提出升力式高超声速飞行器气动布局，并采用工程估算方法获得飞行器气动特性数据。针对最大射程、最小射程和跳跃弹道等典型再入弹道进行沿弹道的模态稳定性分析，得到高超声速再入弹道高度模态、沉浮模态和短周期模态稳定性沿弹道的变化特征。从稳定性的角度，对弹道优化提出建议：应避免所设计的弹道产生太大的跳跃，即使是牺牲一些射程上的性能，因为跳跃会使短周期模态和沉浮模态产生更多的不稳定特征根。
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.
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