Bifurcation Analysis of Nonlinear Aircraft Dynamics

Abstract

A new approach is presented for analyzing nonlinear and high-a 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 presented, using numerical techniques based on parametric continuation. It is shown 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-a phenomena, especially spin-related behavior, is discussed. RENDS in fighter aircraft design over the past few decades have resulted in configuration s noted for their high speed and performance capability. The cost of achieving this capability has been a drastic, often fatal loss of positive control of the aircraft as the pilot operates at or near the extremes of the flight envelope. This is especially true for aircraft motion at high angles of attack (a), where large deviations both in the state and control variables limits the application of the usual linearized analysis techniques. There is a conspicuous lack of techniques for analyzing global stability and large maneuver response of aircraft. While certain phenomena (e.g., roll coupling) have been analyzed in an isolated manner, there exists a clear need for a unified approach to analyze systematically global aircraft behavior at high a.