The Research of Chaos Mapping Method with Infinite Collapses to Mechanism Synthesis
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. The property of chaos sequences produced by one dimensional simple chaos mapping method with infinite collapses in finite interval was analyzed. For the first time, a new method based on utilizing one dimensional chaos mapping method with infinite collapses to obtain locate initial points to find all solutions of the nonlinear questions was proposed. The numerical examples in linkage synthesis and approximate synthesis show that the new method is correct and effective.
Helen Zhang, Gang Shen and David Jin
Q. Y. Liu et al., "The Research of Chaos Mapping Method with Infinite Collapses to Mechanism Synthesis", Advanced Materials Research, Vols. 204-210, pp. 79-82, 2011