Adecarlos Carvalho
Av. dos Portugueses, 1966, Bacanga, Sao Luıs, MA, Brasil
Departamento de Matematica, Universidade Federal do Maranhao
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.

Carvalho A. C., Cabral H. E.
Lyapunov Orbits in the $n$Vortex Problem on the Sphere
2015, vol. 20, no. 3, pp. 234246
Abstract
In the phase space reduced by rotation, we prove the existence of periodic orbits of the $(n + 1)$vortex problem emanating from a relative equilibrium formed by $n$ unit vortices at the vertices of a regular polygon at a fixed latitude and an additional vortex of intensity κ at the north pole when the ideal fluid moves on the surface of a sphere.

Carvalho A. C., Cabral H. E.
Lyapunov Orbits in the $n$Vortex Problem
2014, vol. 19, no. 3, pp. 348362
Abstract
In the reduced phase space by rotation, we prove the existence of periodic orbits of the $n$vortex problem emanating from a relative equilibrium formed by $n$ unit vortices at the vertices of a regular polygon, both in the plane and at a fixed latitude when the ideal fluid moves on the surface of a sphere. In the case of a plane we also prove the existence of such periodic orbits in the $(n+1)$vortex problem, where an additional central vortex of intensity κ is added to the ring of the polygonal configuration.
