Chaotic Newton Iterative Method to Mechanism Synthesis Based on Chaotic Sequences Produced by Anti-control of Chaos in Induction Motor Motion

Discovery of dynamical chaos is one of the main achievements in the modern science and how to expand its application has significant meaning for the development of modern science. Many questions in natural science and engineering are transformed into finding the solutions of nonlinear equations. Newton iterative method is an important technique of one dimensional and multidimensional variables and iteration process exhibits sensitive dependence on initial guess point. For the first time, a new method of finding all solutions of nonlinear equations is proposed, in which initial points are taken as chaotic sequences generated by anti-control of chaos in induction motor motion. The range of chaotic variables is bigger than that in other methods and the chaotic variables are not emanative, so the computing time is less than other methods. The numerical examples in linkage synthesis and approximate synthesis show that the method is correct and effective.