机构综合的刚体运动混沌反控制方法研究

The Research of Newton Iterative Method based on Anti-control of Chaos in Rigid Body Motion of Mechanism Synthesis

混沌是现代科学的主要成就之一,扩展混沌的应用对现代科学的发展有重要意义。自然科学与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。利用刚体运动混沌反控制方法产生牛顿迭代法的敏感初始点,首次提出了基于刚体运动混沌反控制的牛顿迭代法求解非线性方程组的新方法。该方法产生的混沌变量范围大,且不会发散,计算时间少。机构综合与近似综合实例表明该方法的正确性与有效性。

The discovery of dynamical chaos is one of the main achievements in the modern science and how to expand its application has important significance to the development of modern science.Many questions in natural science and engineering are transformed into nonlinear equations to be found,Newton iterative method is an important technique to one dimensional and multidimensional variables and iterative process exhibits sensitive dependence on initial guess point.For the first time,a new method to find all solutions based on utilizing anti-control of chaos in rigid body motion to obtain locate initial points to find all solutions of the nonlinear questions was proposed.The range of chaotic variables is bigger than other methods and the chaotic variables are not emanative,so the computing time is less than other.The numerical examples in linkage synthesis and approximate synthesis show that the method is correct and effective.