This article is cited in 2 papers

Parametric Resonance of a Charged Pendulum with a Suspension Point Oscillating Between Two Vertical Charged Lines

Adecarlos C. Carvalho^a, Gerson C. Araujo<sup>b

a</sup> Department of mathematics, Universidade Federal do Maranhão, Av. dos Portugueses, 1966 São Luís-MA, Brazil
^b Department of mathematics, Universidade Federal de Sergipe, São Cristovão, Brazil

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.

Keywords: planar charged pendulum, parametric resonance, Hamiltonian systems, Deprit – Hori method.

MSC: 37N05, 70H14, 70J40, 70J25

Received: 02.11.2022
Accepted: 13.05.2023

Language: English

DOI: 10.1134/S156035472303005X

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