含参量的非线性微分代数系统的程序算法与应用

摘要

目的 针对含未知参量的非线性微分代数系统,建立有效程序分析的方法.方法 以每个时间点上未知乘子参量为设计变量,以微分方程和代数方程约束条件关系为目标函数,构建确定未知乘子参量计算的优化问题,并编制未知乘子参量函数和状态量函数的按时间步长逐步分析计算程序.结果 分析了双摆动力学算例,获得精确的计算结果,表明了笔者提出算法的正确性.结论 提出的程序算法解决了复杂微分代数系统的直接求解,为复杂工程实际问题的计算与应用提供了良好条件.%As to nonlinear differential algebraic systems with unknown multiplier parameters, making unknown multiplier parameters on each time point as design variable, constraint relations between differential equations and algebraic equations as the objective function, optimization problem by step about unknown multiplier parameters is set up;computing program is proposed to salve unknown parameters and state variables.Double-pendulum dynamics, as an example, is analyzed through the program, and correctness of results is showed.The method will be used for solving complex engineering problems.