Oscillation susceptibility analysis along the path of longitudinal flight equilibriums

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 δe¯<δe¯, having the property that if δe∉[δe¯,δe¯], then the angle of attack αα and the pitch rate qq oscillate with the same period, while the pitch angle θθ increases (decreases) tending to +∞(−∞). The behavior of the aircraft is simulated in the simplified model when the elevator deflection δeδe varies in the range (δe¯,δe¯) and when δeδe 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.