Topological analysis on the effects of unsteady aerodynamics on motion of aircraft

To study the global effect of unsteady aerodynamics on the aircraft motion including information of equilibria, periodic orbits, turn points, static bifurcations and Hopf bifurcations, topological structure diagrams were computed, which were based on the 6-degree-of-freedom model of motion and an unsteady aerodynamic model of the derivative type. The mechanism of the effect was further abstracted by the evaluation of the loci of the Jacobian matrix eigenvalues and by time-dependence simulations. As the results show, unsteady aerodynamics has a great effect on oscillatory unstable motion and can delay the unstable trend and Hopf bifurcations. However, unsteady aerodynamics has little effect on monotonously unstable motions. Stable periodic motions such as wing-rock and oscillatory spin tend to be suppressed or the amplitudes tend to be lessened due to the rotational damping of the unsteady aerodynamic delay.