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基于等效小参数法基本思想 ,应用分解法原理 ,通过引入逆算符和选择合适的线性与非线性算子 ,建立了一类非线性动态系统周期解的逆算符表达的递推算法 ,并利用 Mathematica计算机代数语言开发出相应的软件系统 ,实现了该算法的计算机自动求解。利用该软件系统 ,可方便快速地求出周期解的解析表达式。文中给出了计算实例 ,并将算法所得结果与四阶 Runge-Kutta数值方法的计算结果作了比较。理论和实例计算结果表明 ,该软件系统通用性强、精度高 ,是进行某类非线性动太民电路分析和计算的有力工具
Based on the basic idea of equivalent small parameter method, a recursive algorithm of inverse operator expression for periodic solutions of nonlinear dynamic systems is established by introducing inverse operators and selecting suitable linear and nonlinear operators. Mathematica computer algebraic language to develop a corresponding software system to achieve the automatic calculation of the computer algorithm. Using this software system, the analytical expressions of periodic solutions can be easily and quickly obtained. The calculation examples are given in the paper, and the results of the algorithm are compared with those of the fourth-order Runge-Kutta numerical method. The theoretical and practical results show that the software system is versatile and accurate, and it is a powerful tool for the analysis and calculation of a certain kind of nonlinear moving terrains