Sensitivity of trajectory stability estimated by Lyapunov characteristic exponents

Abstract

This work discusses the use of Lyapunov characteristic exponents for stability evaluation, and the analytical estimation of their sensitivity to parameters of the problem. The parametric sensitivity of the stability is formulated to provide a methodology for robustness analysis and design of dynamical systems with a complexity level varying from linear time invariant to nonlinear, non-autonomous. Characteristic exponents estimation and the analytical formulation of their sensitivity are based on the discrete QR decomposition method. The proposed methodology is illustrated considering the flapping of a helicopter blade, and helicopter ground resonance with one damper inoperative and with nonlinear blade dampers. Some aspects of characteristic exponents and sensitivity estimation from problems with complex conjugated modes, which are typical of mechanical and aerospace systems, are discussed.