首页|A solution method for decomposing vector fields in Hamilton energy
A solution method for decomposing vector fields in Hamilton energy
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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.
Hamilton energydynamical systemsvector fieldexterior differentiation
赵昕、易鸣、魏周超、朱媛、鹿露露
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School of Mathematics and Physics,China University of Geosciences,Wuhan 430074,China
National Natural Science Foundation of ChinaNational Natural Science Foundation of ChinaNational Natural Science Foundation of China
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