Shil'nikov homoclinic dynamics and the escape from roll autorotation in an F-4 model

An investigation is undertaken into the nonlinear dynamics of an 8th-order model for the F-4J fighter aircraft in a neighbourhood of its autorotation flight regime. This regime is characterized by high roll rates with no roll control inputs. It is found that the basic state goes unstable via a supercritical Hopf bifurcation as the value of stabilator (the pitch axis control surface) is increased (i.e. control column pushed forward). The ensuing stable limit cycle behaviour is itself destroyed at a higher stabilator value in a certain homoclinic bifurcation first analysed by Shil'nikov. A careful numerical continuation analysis is performed using spline interpolation of the tabulated data in the model. The limit cycle is found to reach infinite period along a complex wiggly bifurcation curve, as predicted by the theory of Shil'nikov homoclinic orbits. Several period-doubling and secondary-Hopf (torus) bifurcations are discovered. Direct simulation of the aircraft dynamics, using linear interpolation of the data, is shown to give good agreement with the continuation results. It is found that the homoclinic bifurcation marks an escape from autorotation. That is, varying stabilator slowly through the critical value results in a jump from oscillatory autorotation to symmetric flight. Possible implications of these results for other flight phenomena are discussed.