陀螺系统特征值问题的一些探讨

Research on Eigenvalue Problems of Gyroscopic Systems

陀螺系统特征值问题是在转子动力学中提出的一个典型的数学问题。它的研究一直受到力学界的重视。研究它具有较大的理论意义和工程应用价值。作为本专题的第一部分，本文探讨三维旋转法本身存在的问题。指出三维旋转法不是对任何反对称矩阵都是合适的，而应有条件地应用它。

Eigenvalue problem of gyroscopic systems is a typical mathematical problem derived in rotor dynamics.It is paid attention to in science and technology.Research on the above problems is valuable in the vibration theory and engineering application.This paper is the first part of the topic in which the defect of the 3-d rotation method for solving gyroeigenvalue problems is presented.It is pointed out that the 3-d rotation method is not efficient for any skew symmetric matrices and must be applied conditionally.