On the Periodic Auto–Oscillations of an Electric Circuit with Periodic Imperfections on Its Variables

Abstract

Abstract:The aim of the present paper is to study the periodic auto-oscillations of an electric circuit with periodic imperfections on its variables composed by three condensers, one of them without charge, and two bobbins. We model this system by the Lagrangian approach using the morphology of the Hill problem and the main tool used for proving the results is the averaging theory of dynamical systems.

On the periodic orbits of the perturbed Wilberforce pendulum

“…For doing this we shall use the averaging theory of dynamical systems (see the Appendix for more details). We have been inspired by other works where these techniques have been used for studying other perturbed dynamical problems; see for instance Basu and Gewei (2011), Bustos et al (2013), Bustos et al (2014), Gao et al (2013), Guirao et al (2013a), and Guirao et al (2013b).…”

The Circular Hill Problem Regarding Arbitrary Disturbing Forces: The Periodic Solutions that are Emerging from the Equilibria

“…In Section 2, Theorem 1 will be proved using the averaging theory (see [13][14][15][16][17][18]). In the next corollary, an application of Theorem 1 is shown, whose proof is implemented in Section 3.…”