一类四维幂零向量场的超规范形及应用  

HYPERNORMAL FORM FOR A CLASS OF FOUR-DIMENSIONAL NILPOTENT VECTOR FIELDS AND ITS APPLICATION

作　　者：寇力英 李静[1] 张伟[2] 奚帅杰 Kou Liying;Li Jing;Zhang Wei;Xi Shuaijie(College of Applied Sciences,Beijing University of Technology, Beijing 100124, China;College of Mechanical Engineering and Applied Electronics Technology, Beijing Universityof Technology, Beijing 100124, China;College of Science, Civil Aviation University of China, Tianjin 300300, China)

机构地区：[1]北京工业大学应用数理学院,北京100124 [2]北京工业大学机械工程与应用电子技术学院,北京100124 [3]中国民航大学理学院,天津300300

出　　处：《动力学与控制学报》2019年第2期159-167,共9页Journal of Dynamics and Control

基　　金：国家自然科学基金资助项目(11772007,11372014,11290152);北京市自然科学基金资助项目(1172002)~~

摘　　要：研究一类具有对称性质的四维幂零向量场的超规范形问题,并将其应用于具有实际工程背景的高维非线性动力学模型的简化.发展与完善由Sanders、Baider和KOW提出的规范形进一步简化的理论,利用线性次数函数、多重李括号与分块矩阵的新记号表示相结合的方法,分别获得四维幂零向量场3次、5次截断的超规范形的一般形式,并将超规范形理论应用于研究环型桁架卫星天线模型的化简问题.本文通过引入并完善大尺寸分块矩阵的新记号表示方法,获得一种处理大尺寸分块矩阵运算的新方法,简化繁琐的大尺寸矩阵的运算,为后续的研究带来便利条件.In this paper,we mainly focus on the hypernormal form for a class of four-dimensional nilpotent vector fields,and the results are applied to simplify the practical engineering models in the high-dimensional nonlinear dynamics. We improve and develop the further reduction theory of the normal form proposed by Sanders,Baider and KOW,and based on the method of linear grading function,multiple Lie bracket and the new notations for block matrices,we obtain the three order and the five order hypernormal form,respectively,and then the results are applied to simplify the circular truss antenna models. The introduction of the new notations for block matrices gives a new method for dealing with the calculation of big size block matrices,which brings conveniences for the later research.

关 键 词：四维幂零向量场 超规范形 线性次数函数 多重李括号 

分 类 号：O19[理学—数学]