首页|期刊导航|哈尔滨工业大学学报（英文版）|Newton chaos iteration method and its application to mechanism kinematics synthesis
哈尔滨工业大学学报（英文版）2007，Vol.14Issue(1)：13-17,5.
Newton chaos iteration method and its application to mechanism kinematics synthesis
Newton chaos iteration method and its application to mechanism kinematics synthesis
摘要
Abstract
Many questions in natural science and engineering can be transformed into nonlinear equations.Newton iteration method is an important technique to one dimensional and multidimensional variables and iteration itself is very sensitive to initial guess point. This sensitive area is the Julia set of nonlinear discrete dynamic system which Newton iteration method forms. The Julia set, which is the boundaries of basins of attractions,displays the intricate fractal structures and chaos phenomena. By constructing repulsion two-cycle point function and making use of inverse image iteration method, a method to find Julia set point was introduced. For the first time, a new method to find all solutions was proposed based on utilizing sensitive fractal areas to locate the Julia set points to find all solutions of the nonlinear questions. The developed technique used an important feature of fractals to preserve shape of basins of attraction on infinitely small scales. The numerical examples in linkage synthesis showed that the method was effective and correct.关键词
chaos/fractal/Julia set/link mechanism/nonlinear equationsKey words
chaos/fractal/Julia set/link mechanism/nonlinear equations分类
机械制造引用本文复制引用
LUO You-xin,GUO Hui-xin..Newton chaos iteration method and its application to mechanism kinematics synthesis[J].哈尔滨工业大学学报（英文版）,2007,14(1):13-17,5.基金项目
Sponsored by the Scientific Research Fund of Ministry Education( Grant No. 02t08) ,and the Key Seientific Research Fund of Hunan Provincial Education Department (Grant No. 04A036), and the Grant of the 11-th Five-year Plan for Key Construction Disciplines Mechanical Design and Theory of Hunan Province. （ Grant No. 02t08）
