Do we Really Need to Study Rotorcraft as Linear Periodic Systems?

This work discusses the application of Lyapunov Characteristic Exponents as a means of generalizing rotorcraft stability analysis. Stability estimation of linear time invariant and linear time periodic systems relies on eigenanalysis of special state transition matrices and implies simplifications on the nonlinear non-autonomous equations that govern rotorcraft stability. Lyapunov Characteristic Exponents provide quantitative information on the stability of nonlinear non-autonomous dynamical systems. Stability estimation using Lyapunov Characteristic Exponents does not require a special reference solution and agrees with the eigensolution of linear time invariant and Floquet-Lyapunov analysis of linear time periodic systems. Thus, they represent a natural generalization of conventional stability analysis. The Discrete QR method is used to practically estimate the Lyapunov Characteristic Exponents. The method is applied to rotorcraft related problems. Results are correlated with usual methods for linear time invariant and time periodic problems when possible.