Gerson Araujo
Federal University of Sergipe
Publications:
Carvalho A. C., Araujo G. C.
Parametric Resonance of a Charged Pendulum with a Suspension Point Oscillating Between Two Vertical Charged Lines
2023, vol. 28, no. 3, pp. 321331
Abstract
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.

Araujo G. C., Cabral H. E.
Parametric Stability of a Charged Pendulum with an Oscillating Suspension Point
2021, vol. 26, no. 1, pp. 3960
Abstract
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 DepritHori method to construct the boundary surfaces of the stability/instability regions.
