非线性动力系统周期解的反解型预测追踪算法

Inverse Tracing of Periodic Solutions for Nonlinear Dynamic Systems

提出一种对非线性动力系统周期解进行预测追踪的新型算法．它利用系统周期解的稳态及瞬态信息、反解雅可比矩阵，实现对系统周期解的预测追踪．同时，利用反解得出的雅可比矩阵，还可以得出系统周期解的Ｆｌｏｑｕｅｔ乘子，判别其非线性稳定性．与现有的此类算法相比，新算法在实施时，所需要的信息均可通过对系统周期解的未扰及受扰运动的观测获得，因而具有广泛的适应性．文中以非线性轴承转子系统为例，实现了周期解的预测追踪及非线性稳定性判别，说明了新算法的有效性．

Tracing method of periodic solutions for nonlinear dynamic systems is considered. The steady state and transient state information is used to solve the Jacobi matrix, and to trace the periodic solution. The Floquet multiplier can be used to determine the nonlinear stability. Compared with other algorithm, the proposed method has the advantage that all the needed information can be obtained from online observations. Using nonlinear bearing rotor systems as an example, the T periodic solution is traced to illustrate the method of solution.