Rotor-bearings systems applied widely in industry are nonlinear dynamic systems of multi-degree freedom.Stability analysis of this kind of systems always is concerned by engineer.Modern concepts on design and maintenance call for quantitative stability analysis.In the present paper, using trajectory based stability-preserving dimensional-reduction;a quantitative stability analysis method for rotor systems is presented.At first, an 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.