机构综合的牛顿混沌迭代方法研究

The Research of Newton Chaos Iteration Solution Method and Its Application to Mechanism Synthesis

工程中的许多问题都可以转化为非线性方程组的求解问题,牛顿迭代法是重要的一维及多维的迭代技术,其迭代本身对初始点非常敏感,该敏感区是牛顿迭代法所构成的非线性离散动力系统Ju lia集,提出了用排斥二周期点寻找牛顿迭代函数的Ju lia点的求解方法,利用非线性离散系统在其Ju ilia集出现混沌分形现象的特点,首次提出了基于混沌的牛顿迭代的非线性方程组求解新方法。对平面曲柄—滑块机构综合进行了研究,算例表明该方法的正确性与有效性。

Many problem in engineering can be transformed into nonlinear equations for solution, Newton iterative method is an important technique to one dimensional and multidimensional variables and a nonlinear discrete dynamtic process that exhibits sensitive dependence on initial guess point. This sensitivity has a fractal nature. The Julia set of Newton iterative function is the sensitive area and is also the boundaries of basins of attractions display the intricate fractal structures and chaos phenomena. By constructing repulsion two-cycle point function and making use of inverseimage iterative methods, a method to find Julia set point is introduced. For the first time, a new method to find all solutions based on utilizing sensitive fractal areas to locate the Julia set point to find all solutions of the nonlinear questions is proposed. The developed technique uses an important feature of fractals to preserve shape of basins of attraction on infinitely small scales. The numerical examples in planar crank-slide mechanisms shows that the method is effective .