非线性负阻尼极限环型角位移振荡运动定量分析

从某飞行器两次飞行记录的俯仰角θ、偏航角Ψ观测值出发，分别采用对Van der Pol方程描述的θ和Ψ的角位移振荡运动微分方程进行气动参数辨识，和对观测值θ-狋、Ψ-t曲线的外包络线进行参数拟合两种分析方法，对该飞行器的角位移振荡运动特性进行了定量分析。两种分析方法取得了较为一致的结果，并证明该飞行器飞行中出现的锥形振荡运动是典型的非线性负阻尼极限环型的振荡运动，获得了非线性负阻尼极限环型气动阻尼力矩的典型表达式。分析结果表明非线性负阻尼极限环类型的气动阻尼能够导致飞行器出现动不稳定。

Quantitative analysis on non-linear negative the angular oscillation of damping limit cycle

Quantitative analysis for angular oscillation is conducted,from the observations of pitch angleθand yaw angleΨof an aircraft in two flight tests.Aerodynamic parameter identifica-tion for Van der Pol equation θ＆#183;＆#183;= C00θ＋Cm1 （1-C11θ2 ）θ＆#183; and ＆#183;Ψ＆#183;= C00Ψ＋Cn1 （1-C22Ψ2 ）Ψ＆#183; de-scribing angular oscillations in pitch and yaw planes respectively,and parameter fitting for the outer envelope curve ofθ-t and Ψ-tobservations,are both carried out.The fitting and parameter identification curves of two flight tests both show good agreement with observations,which means the fitting and parameter identification results are both reliable.All the parameters,inclu-ding Cm1 ,C11 ,Cn1 and C22 ,obtained from parameter identification are similar to those from fit-ting of outside envelope curves in the two flight tests,except a bit difference for C11 by the two methods for the first flight test.The conclusion can be made that the angular oscillations in pitch and yaw planes are the typical non-linear negative damping limit cycle type oscillation,for Cm1 ,C11 ,Cn1 and C22 are all positive while C00 is negative.And that indicates the coning oscillation of the aircraft is stimulated by the aerodynamic damping moment of non-linear negative damping limit cycle type.The typical expression of the aerodynamic damping moment of non-linear nega-tive damping limit cycle type can be acquired according to parameters above.Finally,it is verified that dynamic instability of aircrafts can be brought by the aerodynamic damping moment of non-linear negative damping limit cycle type.