Nonlinearity Index Theory for Aircraft Dynamic Assessment

This paper introduces the nonlinearity index theory for assisting aircraft flight dynamics. The nonlinearity index theory was originally developed for orbital mechanics applications within the context of an initial value problem, while aircraft dynamic systems more commonly experience an input excitation as well as sensitivity to initial conditions. This current research proposes an algorithm for applying the index to aircraft dynamics. The algorithm starts by gridding down the flight envelope to a set of points. Around each point, an elliptical subregion is defined as ratios of the altitude and Mach number bands. A set of nominal linear models is then generated at each point. The maximum deviation of each nominal linear model from the equivalent linear models over the local subregion is presented as the basis for various nonlinear index measures. Visualizing these metrics over the entire flight envelope delivers a criterion to predict and identify flight regions of nonlinear phenomena such as limit cycling, which can be easily overlooked from comparing linear and nonlinear simulations.