Redução do número de graus de liberdade de sistemas Hamiltonianos: aplicações a problemas de Mecânica Celeste

• Ano de defesa: 2019
• Autor(a) principal: Ospina, Daniela Cortes [UNIFESP]
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de São Paulo (UNIFESP)
• Palavras-chave em Português: Hamiltonian System; First Integrals; Differential Equations; Two-Body Problem; Sistemas Hamiltonianos; Integrais Primeiras; Equações Diferenciais; Problema De Dois Corpos
• Link de acesso: https://sucupira.capes.gov.br/sucupira/public/consultas/coleta/trabalhoConclusao/viewTrabalhoConclusao.jsf?popup=true&id_trabalho=8437856; https://repositorio.unifesp.br/handle/11600/59381

Often, dynamical systems derived from Celestial Mechanics involving both translational and rotational motion - or both simultaneously - are treated using Hamiltonian formulation. In these problems, disturbances are considered by conservative forces. The differential equations involved are generally nonlinear, for which, except in some particular cases, it is not possible to obtain a closed analytical solution. In the present work, we will use classical theorems to study some of these systems, looking for first integrals that can reduce the number of degrees of freedom of the same. We will apply the studies done to the problem of the orbital motion of an artificial satellite around a central body. In this we will consider, besides the problem of two bodies, perturbations due to the non distribution of mass of the central body, as well as the gravitational attraction for a third body. At the end we present the construction of Adelphic integrals for Hamiltonian systems, whose Hamiltonian function is not explicitly time dependent and is expressed in trigonometric series.