Gerson Araujo

Federal University of Sergipe


Carvalho A. C., Araujo G. C.
In this study, we analyze a planar mathematical pendulum with a suspension point that oscillates harmonically in the vertical direction. The bob of the pendulum is electrically charged and is located between two wires with a uniform distribution of electric charges, both equidistant from the suspension point. The dynamics of this phenomenon is investigated. The system has three parameters, and we analyze the parametric stability of the equilibrium points, determining surfaces that separate the regions of stability and instability in the parameter space. In the case where the parameter associated with the charges is equal to zero, we obtain boundary curves that separate the regions of stability and instability for the Mathieu equation.
Keywords: planar charged pendulum, parametric resonance, Hamiltonian systems, Deprit – Hori method
Citation: Carvalho A. C., Araujo G. C.,  Parametric Resonance of a Charged Pendulum with a Suspension Point Oscillating Between Two Vertical Charged Lines, Regular and Chaotic Dynamics, 2023, vol. 28, no. 3, pp. 321-331
Araujo G. C., Cabral H. E.
We consider a planar pendulum with an oscillating suspension point and with the bob carrying an electric charge $q$. The pendulum oscillates above a fixed point with a charge $Q.$ The dynamics is studied as a system in the small parameter $\epsilon$ given by the amplitude of the suspension point. The system depends on two other parameters, $\alpha$ and $\beta,$ the first related to the frequency of the oscillation of the suspension point and the second being the ratio of charges. We study the parametric stability of the linearly stable equilibria and use the Deprit-Hori method to construct the boundary surfaces of the stability/instability regions.
Keywords: charged pendulum, parametric stability, boundary surfaces of stability, Hamiltonian system
Citation: Araujo G. C., Cabral H. E.,  Parametric Stability of a Charged Pendulum with an Oscillating Suspension Point, Regular and Chaotic Dynamics, 2021, vol. 26, no. 1, pp. 39-60

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