驻定系统在其特征方程以零为重根时的稳定性

Stability of Stationary System in the Case of Its Characteristic Equation with r-Multiple Zero Roots

本文讨论了驻定系统在其一次近似特征方程以零为重根,但无正实根及纯虚根的情况下零解的稳定问题,得到了判断该系统零解为稳定或为不稳定的充分条件。在第一临界情况下关于稳定或不稳定的结果,是本文定理当 r=1的推论。

This paper discusses the problem of the stability of stationary motion in the case that the characteristic equation of its first approximationhas r-multiple zero roots,and arrives at sufficient conditionshat can judge the trivial solution of the discussed system to be stableor not.The results about stability or un unstability in the firstcritical case are corrollarics of the theorems in thes paper when r=1.