On the appearance of a Hopf bifurcation in a non-ideal mechanical problem |
| |
Authors: | M rcio Jos Horta Dantas,Jos Manoel Balthazar |
| |
Affiliation: | a Faculdade de Matemática, UFU, 38408-100, Uberlândia, MG, Brazil;b Departamento de Estatística, Matemática Aplicada e Computação, Instituto de Geociências e Ciências Exatas, CP 178, UNESP 13500-230, Rio Claro, SP, Brazil;c Mechanical Design Department, UNICAMP, 13083-970, Campinas, SP, Brazil |
| |
Abstract: | In this paper we studied a non-ideal system with two degrees of freedom consisting of a dumped nonlinear oscillator coupled to a rotatory part. We investigated the stability of the equilibrium point of the system and we obtain, in the critical case, sufficient conditions in order to obtain an appropriate Normal Form. From this, we get conditions for the appearance of Hopf Bifurcation when the difference between the driving torque and the resisting torque is small. It was necessary to use the Bezout Theorem, a classical result of Algebraic Geometry, in the obtaining of the foregoing results. |
| |
Keywords: | Hopf bifurcation Non-ideal problems Center manifold |
本文献已被 ScienceDirect 等数据库收录! |
|