Abstract
In this chapter, a route of periodic motions to chaos in a nonlinear Jeffcott rotor system are studied through an implicit mapping method. The continuous nonlinear rotor system is discretized to construct implicit mappings. Through the mapping structures, semi-analytical solutions of periodic motions are obtained. Bifurcation trees of period-1 motion to chaos are presented. The stability and bifurcations of periodic motions are discussed through the eigenvalue analysis. Numerical simulations of periodic motions are completed with initial conditions from the analytical predictions. Phase trajectories, displacement orbits and velocity planes are presented for comparison of numerical and analytical results.
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