Navegando por Palavras-chave "First Integrals"

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    Redução do número de graus de liberdade de sistemas Hamiltonianos: aplicações a problemas de Mecânica Celeste
    (Universidade Federal de São Paulo (UNIFESP), 2019-09-20) Ospina, Daniela Cortes [UNIFESP]; Moraes, Rodolpho Vilhena De [UNIFESP]; Universidade Federal de São Paulo (UNIFESP)
    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.