ESTABILIDADE PARAMÉTRICA DE UM PÊNDULO CARREGADO COM PONTO DE SUSPENSÃO OSCILANTE ENTRE DUAS RETAS HORIZONTAIS COM DISTRIBUIÇÃO UNIFORME DE CARGAS ELÉTRICAS

Abstract

In this study, we analyzed a planar mathematical pendulum with a suspension point that oscillates vertically, governed by a harmonic law. The pendulum bulb is electrically charged and is located between two horizontal lines with uniform distribution of electrical charges, both equidistant from the suspension point. We determine the Hamiltonian formalism of this mechanical phenomenon, then we find two equilibrium points, and we analyze the linear stability of this system. This dynamic system has three dimensionless parameters, namely, μ related to the electrical charge, the parameter εreferring to the amplitude of the suspension point and α arising from the system frequency. We investigate the parametric stability of the equilibrium points, finally, we display the surfaces that separate the regions of stability and instability in the parameter space, using the Deprit -Hori method.

Keywords: charged pendulum; parametric stability; linear stability; boundary surfaces of stability, Hamiltonian system.