Existence of oscillatory solutions along the path of longitudinal flight equilibriums of an unmanned aircraft, when the automatic flight control system fails

The motion around the center of mass of a rigid unmanned aircraft, whose flight control system fails, in an “Aero Data Model In a Research Environment” is described, by a set of nine nonlinear ordinary differential equations. The longitudinal flight with constant forward velocity is described by a subset of three nonlinear differential equations, obtained from the general system. In this paper, the existence of oscillatory solutions of this system of three differential equations is proved by means of coincidence degree theory and Mawhin's continuation theorem.