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介07绍了求解非线性自治系统定常解分叉、HOPF分叉问题的扩展方程方法，其基本思想是：根据各种分叉情况的发生条件，对原系统方程适当增加相应的约束方程，从而形成系统动力学特性随某─参数变化时而发生分叉问题的定解条件．文中利用此方法求解了一实际平衡转子─轴承非线性系统随转速变化的单参数族系统的分叉点，结果证明，扩展方程方法在求解转子的半频涡动和油膜荡振方面具有有效的应用价值，能够快速准确地确定转子的失稳转速．
The basic idea of the extended equation method for solving steady-state unbranching and HOPF bifurcation problem of nonlinear autonomous system is as follows: According to the conditions of occurrence of various bifurcation conditions, the corresponding constraint equations are appropriately added to the original system equation so that Form the solution conditions for the bifurcation problem of the system dynamics with time-varying parameters. In this paper, the bifurcation point of a single parametric family system with a balanced rotor-bearing nonlinear system is obtained by using this method. The results show that the extended equation method is effective in solving the half-frequency eddy and oil oscillation of the rotor Application value, can quickly and accurately determine the rotor rotational speed.