非自治系统的全局稳定性

文[1]研究了带有一个非自治项的四阶微分方程的全局稳定性,它推广了[2]的结果。本文研究一般的四阶非自治微分方程 (1)的全局渐近稳定性。对这个方程,我们构造了所需要的函数,并参照文[3][4]的办法,作出了易于检验的判定四阶非自治系统全局渐近稳定的充分条件。     

消振器的数学原理

在工程技术中往往采用消振器来消除自激振荡,使设备或机器不受损坏。本文给出了一个消振器的数学模式我们讨论了如何适当选取方程组(*)的参数c_1,k_1,k_2,使其零解是全局渐近稳定的,得到了方程组(*)的零解全局渐近稳定的若干定理。     

THE MATHEMATICAL PRINCIPLES OF VIBRATION REDUCTOR

In engineering and technology, it is often demanded that self-oscillation.be eliminated.so that the equipment or machinery may not be damaged In this paper, a mathematicalmodel for reducing vibration is given by the following equations:(?)_1+(?)((?)_1) +k_1(x_1-x_2) =0, (?)_2+c(?)_1+k_2(x_2-x_1) =0 (*)We have discussed how to choose suitable parameters c_1, k_1,k_2; of equations (*),so as to make the zero solution to be of global stability. Several theorems on the globalstability of the zero solution of equations (*) are also given.