Abstract: Rotor-bearings systems applied widely in industry are nonlinear dynamic systems of multi-degree-of-freedom.Modern concepts on design and maintenance call for quantitative stability analysis. Using trajectory based stability-preserving,dimensional-reduction,a quantitative stability analysis method for rotor systems is presented.At first,a n-dimensional nonlinear non-autonomous rotor system is decoupled into n subsystems after numerical integration.Each of them has only one-degree-of-freedom and contains time-varying parameters to represent all other state variables.In this way,n dimensional trajectory is mapped into a set of one-dimensional trajectories.Dynamic central point (DCP)of a subsystem is then defined on the extended phase plane,namely force-position plane. Characteristics of curves on the extended phase plane and the DCP's kinetic energy difference sequence for general motion in rotor systems are studied.The corresponding stability margins of trajectory are evaluated quantitatively.By means of the margin and its sensitivity analysis,the critical parameters of the period doubling bifurcation and the Hopf bifurcation in a flexible rotor supported by two short journal bearings with nonlinear suspensionare determined.