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利用哈密顿算子辛自共轭的特点讨论了保守哈密顿体系的摄动问题,给出了哈密顿矩阵的本征值与本征向量的二阶摄动分析方法。即当系统在哈密顿框架下进行较小修改时,不重复求解大型哈密顿矩阵的本征问题,只需在原系统的模态参数基础上进行模态分析即可,这种矩阵摄动法给出了修改后矩阵的二阶本征值和本征向量,为一般线性保守体系的本征摄动求解提出了一个新方法。
The perturbation of the conservative Hamiltonian system is discussed by using the self - conjugate characteristic of the Hamiltonian operator, and the second order perturbation analysis method of the eigenvalues and eigenvectors of the Hamiltonian matrix is given. That is to say, when the system makes minor modifications under Hamiltonian framework, it does not need to repeat the eigenproblem of large-scale Hamiltonian matrix only by modal analysis based on the modal parameters of the original system. The matrix perturbation method After the modified second order eigenvalue and eigenvector of matrix, a new method is proposed for the eigen-perturbation solving of general linear conservative system.