Application of bifurcation analysis and Catastrophe theory methodology (BACTM) to aircraft stability problems at high angles-of-attack

Aircraft dynamic behavior at high angles-of-attack is highly nonlinear and, in the past, there has been a lack of suitable techniques for analyzing the global behavior of nonlinear systems. In this paper an approach based on Bifurcation Analysis and Catastrophe Theory Methodology (BACTM) has been applied to specific jump, hysteresis and limit cycle phenomena such as roll-coupling, pitch-up, wing rock, buffeting, departure and divergence. Four different aircraft have been considered for comparison purposes, and it has been shown how different types of instabilities and families of limit cycles arise as the control variables are varied. A complete representation of the aircraft equilibrium and bifurcation surfaces is given in a nine dimensional space consisting of velocity, roll rate, pitch rate, yaw rate, angle-of-attack, sideslip angle, elevator, aileron and rudder deflections. The use of BACTM for understanding spin entry, spin prevention, spin recovery and stability augmentation at high angles-of-attack are also discussed.