Methods for stability and instability of the solution of one non-linear differential equation

Abstract

When research on instability states of tall and flexible structures is carried out, the solutions of non-linear differential equations have to be investigated. Although the fully analytical solutions of the moving rule of the structures cannot be found, but based on the conditions applied to the parameters of the moving differential equations the authors have studied the characteristics of the solutions when t→∞. Then the instability of the structures may be investigated, and the stability conditions can be concluded. This is the content which this paper would like to present.