Bifurcation and Limit Cycle Analysis of Nonlinear Systems with an Application to Aircraft at High Angles of Attack

A new approach is presented for analyzing nonlinear and high-α dynamic behavior and stability of aircraft. This approach involves the application of bifurcation analysis and catastrophe theory methodology to specific phenomena such as stall, departure, spin entry, flat and steep spin, nose slice, and wing rock. Quantitative results of a global nature are generated using numerical techniques based on parametric continuation. We discuss how our methodology provides a complete representation of the aircraft equilibrium and bifurcation surfaces in the state-control space, using a rigid body model with aerodynamic controls. Also presented is a particularly useful extension of continuation methods to the detection and stability analysis of stable attracting orbits (limit cycles). The use of this methodology for understanding high-α phenomena, especially spin-related behavior, is discussed.