Lyapunov-Kozlov method for singular cases |
| |
Authors: | V Čović D Djurić M Vesković A Obradović |
| |
Institution: | V. (C)OVI(C),D. DJURI(C),M. VESKOVI(C),A. OBRADOVI(C) |
| |
Abstract: | Lyapunov’s first method, extended by Kozlov to nonlinear mechanical systems, is applied to study the instability of the equilibrium
position of a mechanical system moving in the field of conservative and dissipative forces. The cases with a tensor of inertia
or a matrix of coefficients of the Rayleigh dissipative function are analyzed singularly in the equilibrium position. This
fact renders the impossible application of Lyapunov’s approach in the analysis of the stability because, in the equilibrium
position, the conditions of the existence and uniqueness of the solutions to the differential equations of motion are not
fulfilled. It is shown that Kozlov’s generalization of Lyapunov’s first method can also be applied in the mentioned cases
on the conditions that, besides the known algebraic expression, more are fulfilled. Three theorems on the instability of the
equilibrium position are formulated. The results are illustrated by an example. |
| |
Keywords: | instability singular case asymptotic motion potential dissipative force |
本文献已被 CNKI 维普 万方数据 SpringerLink 等数据库收录! |
|