On the existence and stability of periodic orbits in non ideal problems: General results期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

On the existence and stability of periodic orbits in non ideal problems: General results

Authors:	Márcio José Horta Dantas José Manoel Balthazar

Institution:	(1) Faculdade de Matemática, UFU, 38400-902 Uberlndia, MG, Brazil;(2) Departamento de Estatstica, Matemática Aplicada e Computao, Instituto de Geocincias e Cincias Exatas CP 178, UNESP, 13500-230 Rio Claro, SP, Brazil

Abstract:	In this work, motivated by non-ideal mechanical systems, we investigate the following O.D.E. ${\dot{x} = f (x) + \varepsilon g (x, t) + \varepsilon^{2}\widehat{g} (x, t, \varepsilon)}$ , where ${x \in \Omega \subset \mathbb{R}^n}$ , ${g,\widehat{g}}$ are T periodic functions of t and there is a ₀ ∈ Ω such that f ( a ₀) = 0 and f ′( a ₀) is a nilpotent matrix. When n = 3 and f (x) = (0, q (x ₃) , 0) we get results on existence and stability of periodic orbits. We apply these results in a non ideal mechanical system: the Centrifugal Vibrator. We make a stability analysis of this dynamical system and get a characterization of the Sommerfeld Effect as a bifurcation of periodic orbits.

Keywords:	Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) 34C25 70K30
本文献已被 SpringerLink 等数据库收录！