Limit cycle and chaotic behavior in persistent resonance of unguided missiles

Flight dynamics problems that are related to the coupling of yaw, pitch, and rob degrees of freedom of unguided missiles have been the subject of a large number of investigations. special emphasis has been given to persistent resonance and catastrophic yaw phenomena that are caused by nonlinear-induced aerodynamic moments and slight configurational asymmetries, Recently, a rigorous analysis of the persistent resonance problem was performed by using a fifth-order autonomous dynamic system model with linear transverse and nonlinear roll aerodynamics. A simple graphical method was used to locate equilibrium points. Stability of equilibrium points were determined by standard linearization. In this study in addition to equilibrium behavior that was examined by previous investigators, the same dynamic system model was found to exhibit limit cycle (periodic) and chaotic (aperiodic) behavior at steady state. Such behavior was examined by using frequency spectra, Poincare maps, and Lyapunov exponents.