Analysis of the two-degree-of-freedom wing rock in advanced aircraft

The dynamics of wing rock on rigid aircraft having two rotational degrees of freedom area analyzed. Nonlinear mathematical models of the aircraft are developed for the purpose of the analysis. The aerodynamic expressions contained in the models are built by fitting the appropriate aerodynamic data into the model. The nonlinear dynamics are analyzed using a technique combining the multiple time scales method, center manifold reduction principle, and bifurcation theory. Analytical solutions are developed in parametric forms shocking a separation of the fast and slow dynamics. Such solutions have an advantage over numerical solutions in that the important parameters and their effects on wing rock characteristics, such as amplitude and frequency, are easily seen in explicit functional relationships. An excellent agreement between the analytical results and the numerical simulations is demonstrated.