Stability of Nonlinear, Time-Dependent Rotorcraft Systems Using Lyapunov Characteristic Exponents

This work discusses the use of Lyapunov characteristic exponents to generalize rotorcraft stability analysis. Stability analysis of linear time-invariant and time-periodic systems relies on the eigenanalysis of special state transition matrices, which require the simplification of the nonlinear, time-dependent equations that govern rotorcraft aeromechanics. Lyapunov characteristic exponents provide quantitative information on the stability of nonlinear, time-dependent but not necessarily periodic dynamic systems without requiring a special reference solution. Results are consistent with the eigensolution of linear time-invariant and Floquet–Lyapunov analysis of linear time-periodic systems. Thus, the proposed approach represents a natural generalization of conventional stability analysis. The discrete QR method is used to practically estimate Lyapunov characteristic exponents; its economy-size variant is considered to reduce the computational cost for large problems. The method is applied to rotorcraft-related problems; when possible, results are compared with usual methods for linear time-invariant and time-periodic problems