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Through an example of rotor system which has multi-degree of freedom mounted on the nonlinear fluid film
bearings, this paper analyzes the precise integration algorithm, a new numerical solution for high–dimensional nonlinear
dynamics system. The precise integration method has advantages of long step, high precision and absolute stability for
solving nonlinear dynamics equations. To make good use of the method, firstly, the precise integral iterative formula is
given and then the mechanism of controlling high precision and efficiency is discussed. The evolution of precise
integration method is an algorithm with explicit, simple form, self-start, and fast to solve nonlinear dynamics equations.
High power of athwart of Hamiltonian matrix is not needed, so it is convenient in this case. The stability of period
response of nonlinear rotor-bearing system is analyzed by employing the precise integration method. The bifurcation rules
of the period response of the elastic rotor system with multi-degree of freedom are obtained and the chaos of the system is
determined according to the fractal dimension of Poincare mapping of phase space at a certain speed.