Eigenvector similarity metrics for the identification and quantitative study of aircraft dynamic modes

Bifurcation analysis methods can readily provide an indication of unstable equilibrium regions across the aircraft flight envelope. However, the precise nature of the instability – which is essential to inform effective control law design, for example, and especially when modes are not conventional – has to be determined using time consuming numerical time-domain simulations and/or numerous linearisations.
Here we present a novel application of the MACX, an eigenvector similarity metric recently developed in the field of structural dynamics, for the automatic identification of aircraft dynamic modes. In addition, we extend the capabilities of the Dynamical Systems Toolbox (DST), an open source bifurcation analysis tool, to provide the eigenstructure of the system at every point in the bifurcation diagram. These two developments are applied to the exploration of the nonlinear dynamics of NASA’s Generic Transport Model (GTM), with a particular emphasis on the aircraft unstable modal composition in the spiral regions where we find an unconventional oscillatory pitch-roll mode of motion.