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

Quantitative analysis for angular oscillation is conducted, from the observations of pitch angle θ and yaw angle Ψ of an aircraft in two flight tests. Aerodynamic parameter identification for Van der Pol equation θ · · =C₀₀ θ +C_m1 (1-C₁₁ θ²) θ · and Ψ · · =C₀₀Ψ+C_n1 (1-C₂₂ Ψ²) Ψ · describing angular oscillations in pitch and yaw planes respectively, and parameter fitting for the outer envelope curve of θ-t and Ψ-t observations, 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, including C_m1, C₁₁, C_n1 and C₂₂, obtained from parameter identification are similar to those from fitting 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 C_m1, C₁₁, C_n1 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 negative 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.