ABSTRACT
Introduction to various transformation matrices connecting unique axis systems used in flight dynamics, detailed derivation of aircraft six-degree-of-freedom equations of motion and an introduction to industry-accepted bifurcation-theory-based methodology for numerically investigating coupled, non-linear, aircraft equations of motion constitute this chapter. Various sources of non-linearities in an aircraft model and resulting dynamic behaviour are outlined. Usefulness of bifurcation based methods in capturing local as well as global dynamics of non-linear aircraft models is illustrated via examples. Detailed investigation into global non-linear dynamical behaviour resulting from loss of stability of nominal flight conditions and computation of modal behaviour using numerical continuation approach are presented for two real airplane data. Computation of eigenvectors showing participation of states in individual modes at a level flight trim condition, providing the basis for modal approximations is shown as a unique feature of numerical bifurcation analysis. Further, a strong connection between airplane performance and stability is illustrated via analysis of constrained motions of aircraft.
