A solution method for decomposing vector fields in Hamilton energy  

作　　者：Xin Zhao Ming Yi Zhou-Chao Wei Yuan Zhu Lu-Lu Lu 赵昕;易鸣;魏周超;朱媛;鹿露露(School of Mathematics and Physics,China University of Geosciences,Wuhan 430074,China)

机构地区：[1]School of Mathematics and Physics,China University of Geosciences,Wuhan 430074,China

出　　处：《Chinese Physics B》2024年第9期645-653,共9页中国物理B（英文版）

基　　金：the National Natural Science Foundation of China(Grant Nos.12305054,12172340,and 12371506)。

摘　　要：Hamilton energy,which reflects the energy variation of systems,is one of the crucial instruments used to analyze the characteristics of dynamical systems.Here we propose a method to deduce Hamilton energy based on the existing systems.This derivation process consists of three steps:step 1,decomposing the vector field;step 2,solving the Hamilton energy function;and step 3,verifying uniqueness.In order to easily choose an appropriate decomposition method,we propose a classification criterion based on the form of system state variables,i.e.,type-I vector fields that can be directly decomposed and type-II vector fields decomposed via exterior differentiation.Moreover,exterior differentiation is used to represent the curl of low-high dimension vector fields in the process of decomposition.Finally,we exemplify the Hamilton energy function of six classical systems and analyze the relationship between Hamilton energy and dynamic behavior.This solution provides a new approach for deducing the Hamilton energy function,especially in high-dimensional systems.

关 键 词：Hamilton energy dynamical systems vector field exterior differentiation 

分 类 号：O19[理学—数学]