Explorando Sistemas Hamiltonianos II: A Natureza de Pontos de Equilibrio Degenerados

Details Explorando Sistemas Hamiltonianos II: A Natureza de Pontos de Equilibrio Degenerados Explorando Sistemas Hamiltonianos II: A Natureza de Pontos de Equilibrio Degenerados

2007-10-25

arxiv.org/abs/0710.4970v1

Physics

Mathematical Physics

Scientific paper

Neste segundo artigo sobre sistemas Hamiltonianos, apresentamos o metodo da explosao para a determinacao da natureza de pontos fixos (pontos de equilibrio degenerados. Aplicamos o metodo a dois modelos hamiltonianos com um e dois graus de liberdade, respectivamente. Primeiramente, analisamos um sistema formado por um pendulo simples submetido a um torque externo constante T. Em seguida, consideramos um sistema formado por um pendulo duplo com segmentos de comprimentos e massas iguais, tambem submetidos a torques externos constantes e nao nulos. A presenca de pontos de equilibrio degenerados nos casos dos pendulos simples e duplo ocorre para certos valores dos torques externos. In this second article on Hamiltonian systems, we present the blow-up method for the determination of the nature of degenerate fixed points (equilibrium points). We apply the method to two hamiltonian models with one and two degrees of freedom, respectively. Firstly we study a system formed by a simple pendulum submitted to a constant external torque T. Then we consider a system formed by a double pendulum of segments with equal lengths and masses, also submitted to non-vanishing constant external torques. The presence of degenerate equilibrium points in both cases of simple and double pendulums occurs for some values of the external torques.

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