Existence of Gaps on the Path of Equilibriums in Case of Longitudinal Flight with Constant Forward Velocity

Abstract

In this paper it is shown that, in case of longitudinal flight with constant forward velocity of the aircraft considered in [1], on the path of equilibriums there exist gaps and two pieces of the paths are removed. These gaps are hidden when the path of equilibriums is computed by using the decoupled system of three differential equations[1]. That is because the decoupled system is well defined for any value of the Euler pitch angle. The complete system of nine differential equations, from which the system of three differential equations was decoupled, is well defined only for the values of the pitch angle situated in the open interval (−π/2,π/2) . Here first the equilibriums reported in [1] for which the pitch angle is equal to −π/2 or π/2 are removed from the paths and so on the paths gaps appear. After that the equilibriums for which the pitch angle is not in the open interval −π/2,π/2) ƒnare also removed. It is shown that according to the complete system if the elevator deflection takes a value corresponding to a gap, then the aircraft exhibits jump phenomenon.