关键词: 应用数学, 非经典阻尼, 矩阵函数变换, 特征问题, 拟时不变系统

Abstract: In nonclassical damped linear system a matrix function transformation was introduced to get rid of the damping term which is difficult to solve in the systems. The original differential equation with nonclassical damped term is changed into to a quasi timeinvariant equation with a classical damped one. A matrix which has a set of complete eigenvector system can be similar orthogonally to a diagonal one through reduce it to Jordan’s normal form, and based on this property,the reducing matrix was taken as the transformation one. Thus all eigenvalues and eigenvectors of the system can be obtained. At the same time it is know by analysis about matrix characteristic of the similar orthogonally that not only the characteristic value after the transformation is equal to the ones before the transformation and they are independence to time variable of the system, but also the eigenvectors of the formed system can showed the effect of the time variable on original system. The transformation bears clear physical meaning to nonclassical damped linear systems.

Key words: applied mathematics, nonclassical damped system, matrix function transformation, eigenproblem, quasi timeinvariant system