Application of bifurcation theory to the dynamics of flight at high angles of attack

摘要

The chief purpose of this work was to apply contemporary methods of bifurcation theory to the dynamics of flight at high angles of attack. Much of the effort was required to adapt continuation methods for computing the bifurcation curves of steady-state motions as control settings are changed. The complete system of nonlinear equations of motion for a rigid aircraft were used, an eighth order system including the equations for two Euler angles. Special cases of a sixth order system (gravity ignored) and a fifth order system (when the speed is constant) are also accommodated. Three examples were treated in this work: a generic jet fighter, a general aviation canard design (longitudinal motions only); and the F-14 fighter. Bifurcations of steady states were determined and shown to cause instabilities leading to qualitative changes in the state of the aircraft. A longitudinal instability which resulted in a deep stall was determined for the general aviation aircraft. Roll-coupling and high angle of attack instabilities were determined for the F-14. Knowledge of the control surface deflections at which bifurcations occurred was used to either put limits on the surface deflections such that a combination of control surface deflections at which bifurcations occur could not be attained. Simple control systems were included in the aircraft models to determine the effects of the control system on the instabilities of each aircraft. Steady spin modes were determined for each aircraft. A successful recovery technique was determined for the general aviation aircraft, but no successful recovery technique could be found for the F-14.