Teoria da estabilidade paramétrica para sistemas hamiltonianos com aplicação no problema do pêndulo carregado com ponto de suspensão oscilante

Abstract

In this thesis, we present the theory of parametric stability in linear Hamiltonian systems with a degree freedom. Therefore, we provide definitions and results on Hamiltonian systems, symplectic vector spaces and stability of equilibrium points of linear Hamiltonian systems. Subsequently, we analyzed the parametric stability of linear Hamiltonian systems and, with the aid of the Deprit Hori method, constructed the curves that delimit the regions of stability and instability in the plane of the parameters of the Mathieu equation. This text ends with the description and study of the article "Parametric stability of a pendulum loaded with an oscillating suspension point" developed by researchers Hildeberto Eulalio Cabral and Adecarlos Carvalho, as cite adecarlos, in which the construction of the limiting surfaces is conceived regions of stability and instability in the parameter space.