Eigenvalue problem of a large scale indefinite gyroscopic dynamic system
Eigenvalue problem of a large scale indefinite gyroscopic dynamic system
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DOI：
10.1007/s10483-006-0103-z
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发表时间：
2006-01
影响因子：
4.4
通讯作者：
隋永枫;钟万勰
中科院分区：
文献类型：
--
作者：
隋永枫;钟万勰
陀螺动力学系统可以引入哈密顿系统。基于Hamilton陀螺系统的伴随辛子空间迭代法，提出了不定Hamilton函数陀螺系统的伴随辛子空间迭代法，用于求解不定Hamilton函数陀螺系统的特征值问题.利用汉密尔顿陀螺系统的本征值仅为纯虚数或零的性质。将Hamilton函数为负的本征值分离，提出了正定Hamilton函数系统的本征值问题，并利用正定Hamilton函数系统的伴随辛子空间迭代法求解分离的本征值问题.因此，求解了不定哈密顿函数陀螺系统的本征值问题，并给出了两个数值例子，证明了本征值解的精确收敛性。
Gyroscopic dynamic system can be introduced to Hamiltonian system. Based on an adjoint symplectic subspace iteration method of Hamiltonian gyroscopic system, an adjoint symplectic subspace iteration method of indefinite Hamiltonian function gyroscopic system was proposed to solve the eigenvalue problem of indefinite Hamiltonian function gyroscopic system. The character that the eigenvalues of Hamiltonian gyroscopic system are only pure imaginary or zero was used. The eigenvalues that Hamiltonian function is negative can be separated so that the eigenvalue problem of positive definite Hamiltonian function system was presented, and an adjoint symplectic subspace iteration method of positive definite Hamiltonian function system was used to solve the separated eigenvalue problem. Therefore, the eigenvalue problem of indefinite Hamiltonian function gyroscopic system was solved, and two numerical examples were given to demonstrate that the eigensolutions converge exactly.