局部流型分析的哈密顿系统小参数正则变换  

SMALL PARAMETER CANONICAL TRANSFORMATIONS OF HAMILTONIAN SYSTEM FOR THE LOCAL STREAMLINE PATTERN ANALYSIS

作　　者：何士华[1,2] 张立翔[2] 

机构地区：[1]昆明理工大学水力工程系,昆明650051 [2]昆明理工大学工程力学系,昆明650051

出　　处：《动力学与控制学报》2010年第1期29-33,共5页Journal of Dynamics and Control

基　　金：国家自然科学基金(50839003);云南省自然科学基金(2007A030M)资助项目~~

摘　　要：表达二维不可压缩流动的流速分量与流函数关系的微分方程组是典型的具有一个自由度的哈密顿系统.将流函数用Taylor级数展开,应用非线性系统动力学方法对流型及其分岔进行了分析.对退化临界点,基于流动平面的小参数正则变换,导出了流函数的正形表达式和简化的微分方程,并对简化系统的一般特性进行了分析.The differential equations expressing the relations of velocity components and streamfunction for incompressible two-dimensional flow are typical one-degree-of-freedom Hamihonian system. The streamfunction was expanded linear s normal in Taylor series. The streamline patterns and their bifurcations were examined using methods from non- ystem dynamics. Based on the small parameter canonical transformations in the physical flow plane, the form expressions of streamfunction and simplified differential equations were derived for the degenerate critical points. Some general characteristics of the simplified system were analyzed

关 键 词：哈密顿系统 正则变换 临界点 分岔 

分 类 号：O193[理学—数学]