一类阻尼陀螺系统特征值反问题

An Inverse Eigenvalue Problem for Damped Gyroscopic Systems

本文考虑一类阻尼陀螺系统特征值反问题。在假定分析质量矩阵是精确的情况下,运用测量的不完全复模态数据给出了反问题有解的充分必要条件及解的显式表示。在此基础上研究了一个逼近问题,得到了Frobenius范数意义下的最优矩阵。

An inverse eigenvalue problem for damped gyroscopic systems is considered. The solvability conditions for the inverse problem are obtained when the partial information about the eigenvalue and the elgenvector is given under the case that the analytical mass matrix is correct. The explicit expression of the solution to the problem is presented. An optimal approximation problem is discussed in virtue of these results, and the optimal matrices are obtained under the Frobenius norm sense.