Estabilidade espectral no problema carregado de n-corpos - Oliveira, Danielle Aparecida da Silva (2018)
In this work we will study the linear stability of a relative equilibrium in the charged nbody problem. To do this, we will introduce the definition of spectral stability of relative equilibria and we will find conditions necessary to have such stability. We will start the work by showing relevant results in the theory of differentials equations, highlighting some important theorems, such as Existence and Uniqueness Theorem, theorems for linear stability, Floquet’s Theorem and Lyapunov Stability and Instability Theorems. We will do a concise study of Hamiltonian systems, in which we will provide results and definitions that will be of great utility during the dissertation. Among such definitions deserves attention the center configurations (C.C.), since we will show results relating them to the relative equilibria. We will introduce the concept of spectral stability and we will see propositions and theorems for the of n-body problem. An example will be displayed brings a particularity to the charged problem and that makes it very different from the classic n-body problem. Finally, we will apply the results obtained in the charged 3-body problem.