非线性周期非自治系统的 Poincare 型胞映射方法及其应用  

The Poincare Like Cell Mapping Method of Nonlinear Periodic Nonautonomous Systems and Its Application

作　　者：刘恒[1,2] 虞烈[1,2] 谢友柏 姚福生[1,2] 

机构地区：[1]西安交通大学 [2]机械工业部

出　　处：《西安交通大学学报》1998年第4期97-101,共5页Journal of Xi'an Jiaotong University

基　　金：国家自然科学基金;西安交通大学博士基金

摘　　要：通过引入Ｐｏｉｎｃａｒｅ映射的思想，给出一种适用于高维非线性周期非自治动力系统全局特性分析的基于Ｐｏｉｎｃａｒｅ映射的胞映射方法，并通过分析比较，说明传统的胞映射方法实质上是新方法应用中的一个特例．为说明新方法的有效性，用它对不平衡轴承转子非线性动力系统进行了全局特性分析，同时求得了系统存在的周期解及其在各个不同Ｐｏｉｎｃａｒｅ截面上的吸引域，得到了一些新的现象和规律，为建立适用于不平衡轴承转子系统的非线性稳定性准则提供了参考．Through introducing the idea of Poincare Mapping, a Poincare Like Cell Mapping method for global characteristic analysis of higher order nonlinear periodic nonautonomous dynamic systems is presented. Comparison with the conventional Cell Mapping shows the conventional Cell Mapping is a special case of this new method. In order to illustrate the effectivness of Poincare Like Cell Mapping method, the global characteristic of unbalanced bearing rotor system, which is a nonlinear dynamic system, is analyzed using Poincare Like Cell Mapping method. The periodic solutions of this system and their domains of attraction are presented, and some new phenomenan and rules are observed, thus providing some references to establish a new stability rule for nonlinear unbalanced bearing rotor system .

关 键 词：非线性 胞映射 吸引域 稳定性 非自治系统 

分 类 号：TH113.1[机械工程—机械设计及理论]