Existence of heteroclinic orbits in simplified longitudinal flight dynamics

The existence of an infinite chain of heteroclinic orbits connecting saddle-nodes is proved, in the case of a simplified system of differential equations governing the longitudinal flight of an aircraft, using fixed point theory for nonlinear Volterra operators with convolution kernels. Numerical simulations are given and the importance of the obtained results is discussed from the point of view of the appearance of oscillatory behavior in longitudinal flight.