The introduction of the full paper reviews a number of relevant papers in the open literature, points out what we believe to be their shortcomings, and then proposes the analysis mentioned in the title, which we believe is better than previous ones and which is explained in sections 1, 2 and 3. Their core consists of; "Firstly we plan a first track, and then select two representative points in the track, then we make Taylor-expansion on those points, and retain second order to establish the nonlinear perturbed motion model which retains the relevant variables; secondly we use the second order equations eigenvalue perturbation theory to analyze the eigenvalues, which obtained from the linear motion equations and the modified linear equations". Simulation results, presented in Tables 1 through 4, preliminarily show that: (1) if the premise of precision is given, we can, using eigenvalue perturbation theory, determine if we need to modify the eigenvalues of the linear equations or not; ( 2) a corresponding criterion is established and it can be used for complex nonlinear dynamics analysis.%飞行器动力学特性的准确分析与其总体、控制系统设计及准确度分析等有着非常密切的关系.传统的分析方法是基于小扰动假设的线性化方法,即将非线性的扰动运动方程进行线性化处理,利用线性化的方程逼近非线性动力学方程.在小扰动的情况下,这种近似的结果能够保证误差在允许的范围内.然而对于诸如高超声速飞行器这种具有运动范围大、运动过程中受到的各种干扰严重、气动参数的非线性特性明显等特点的飞行器,小扰动假设显然在很多飞行状态下是不合适的,必然会带来扰动运动建模的不准确性,从而导致动态特性分析结果的不准确,对总体、控制系统设计及准确度分析造成错误的结果.文章针对高超声速飞行器在大机动状态下的动态稳定性分析问题,对基于线性化方法得到的平衡特征值是否能够反映非线性特征值所有的运动特征进行研究.首先规划一条航迹,在这条航迹上选择具有代表性的特征点,并在这些特征点上进行泰勒展开,建立保留相关变量高阶项的扰动运动模型；然后利用高阶项信息对线性化方程进行修正,并求出修正后的特征值；利用特征值扰动理论对线性化的扰动运动特征根和基于高阶项修正的扰动运动特征根进行对比分析.结果表明在满足给定精度要求的条件下,可以用范数法则来判定在何种条件(主要考虑扰动的幅值范围)基于小扰动的线性化模型可以适用,在何种条件下必须考虑高阶项的非线性特性.为具有复杂非线性和大扰动值特性的飞行器动态特性分析提供参考依据.
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