一类非线性系统动力特性数值研究

Numerical Study on the Dynamical Characteristic of Nonlinear System

线性化分析方法在研究非线性动力系统时精度不高 ,而且可能会遗漏系统某些重要特性 ,因此有必要改进该方法。文章采用线性化分析和数值分析相结合的方法研究了具有阻尼的单摆系统的动力特性 ,其中 ,线性化分析方法揭示了系统平衡点附近系统的运动特性 ,从而可以判断系统平衡点的性质 ;数值分析方法研究了相平面内非线性系统相轨线的特点。研究表明该方法对研究此类非线性系统动力特性具有精度高、计算方便的优点。

Linearization method will cause low precision and even omit some important characteristics of the system in analyzing nonlinear dynamical systems,so it is essential to improve this method.The paper analyzes the dynamical characteristics of the nonlinear system with linearization and numerical analysis method.Linearization reveals the dynamical characteristics of the nonlinear system at equilibrium point,so that the prosperity of the point can be estimated;and the trajectory of the system in the phase plane is researched by the numeric analysis method.Research result show that this method has advantages of high-precision and convenient calculation in researching the dynamical characteristics of the kind of nonlinear systems.