Approximative Stabilitätsanalyse der nichtlinearen Dynamik von Flugzeugen

A method for the 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 eigenvalue and eigenvector as functions of the deflection from the examined equilibrium. This approach allows the determination of the systems stability properties even beyond the close vicinity of the equilibrium. A test case to verify the robustness of the method and its application to the model of an agile aircraft with highly nonlinear aerodynamics and 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