Simulation to chaos in a rotor

Abstract

Some softwares like Matlab are often employed to simulate physical phenomena. There are many works to observe chaotic motions by simulating trajectories of dynamical systems and plotting complicated phase portraits. In this paper we indicate that those complicated phase portraits plotted by the direct simulation of trajectories may not really exhibit the chaos because some of systems are not autonomous. Considering a nonlinear turbine rotor, we simulate the stable manifold and the unstable manifold and exhibit the chaotic behavior with transversal intersections of the two manifolds.