Stability analysis of the nonlinear dynamics of flexible aircraft

A method for nonlinear analysis of dynamic systems and its application to aircraft is presented. In extension of existing averaging methods this procedure follows the linearizing eigenvalue analysis, but defines the eigenvalues and eigenvectors as functions of the deflection from the examined equilibrium. This approach allows the determination of the systems stability properties beyond the close vicinity of the equilibrium. Its application to the model of a large aircraft with flexible degrees-of-freedom is shown. The analysis shows very good agreement with the results of bifurcational analyses and allows a quantitative prediction of the systems stability behavior even between the branches of the bifurcation diagram. The unstable spiral mode of the flexible aircraft shows the existence of additional stable equilibria in the vicinity of the examined equilibrium due to system nonlinearities.