基于场方法的非线性系统求解

用场方法联立多尺度法求单自由度的非线性系统的近似解．将两个状态方程的一个状态变量看作是另一个状态变量和时间的一个场函数，把原系统化为求解具有初始条件的基本方程，通过多尺度展开，逐个摄动方程求解，获得了振幅和相位的一阶近似微分方程，作为例子，求得了非线性振动系统的一阶近似解，并和数值解进行比较，两者吻合较好。

Approximate solutions of non linar systems based on the field method

This paper studied the asymptotic solutions of non- linear systems with the field method combining with the method of multiple time scales. A state variable in the state equation was regarded as a field function of another state variable and time, then the original system was reduced to the basic equation with initial conditions. Expanding the original equation, we solved step by step the perturbation equations and obtained the first approximate differential equations of the amplitude and phase. As an example, the first analytical solutions of non - linear systems were found, which agreed with the numerical solutions.