Dantas, Márcio José HortaBalthazar, José Manoel [UNESP]2014-05-272014-05-272007-11-01Zeitschrift fur Angewandte Mathematik und Physik, v. 58, n. 6, p. 940-958, 2007.0044-2275http://hdl.handle.net/11449/69945In this work, motivated by non-ideal mechanical systems, we investigate the following O.D.E. ẋ = f (x) + εg (x, t) + ε2g (x, t, ε), where x ∈ Ω ⊂ ℝn, g, g are T periodic functions of t and there is a 0 ∈ Ω such that f (a 0) = 0 and f′ (a0) 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. © 2007 Birkhäuser Verlag, Basel.940-958engBifurcationPeriodic orbitsRegular perturbation theorySommerfeld effectStabilityArtigo10.1007/s00033-006-5116-5Acesso restrito2-s2.0-46649107309