Oscillation susceptibility analysis along the path of longitudinal flight equilibriums

Abstract

In this paper the oscillation susceptibility of an aircraft in a longitudinal flight with constant forward velocity is analyzed in different flight models. Conditions which ensure such a flight, and equations governing the flight are presented. The stability of the equilibriums appearing is analyzed and the existence of Hopf bifurcations and saddle–node bifurcations is researched. For two aircrafts in a simplified model it is shown that saddle–node bifurcations are present and there are no Hopf bifurcations. It is shown that for the elevator deflection there are two turning points δ e ¯ < δ e ¯ , having the property that if δ e ∉ [ δ e ¯ , δ e ¯ ] , then the angle of attack α and the pitch rate q oscillate with the same period, while the pitch angle θ increases (decreases) tending to + ∞ ( − ∞ ) . The behavior of the aircraft is simulated in the simplified model when the elevator deflection δ e varies in the range ( δ e ¯ , δ e ¯ ) and when δ e leaves this range. For one of the aircrafts the analysis is performed also in the not simplified model, showing the differences between the results obtained in different models.