Equilíbrios e estabilidade linear no problema restrito circular de três corpos

• Ano de defesa: 2024
• Autor(a) principal: SILVA, Carlos Eduardo Sousa
• Orientador(a): CARVALHO, Adecarlos Costa
• Banca de defesa: CARVALHO, Adecarlos Costa , CARVALHO, Renata de Farias Limeira , DIAZ, José Claudio Vidal
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal do Maranhão
• Programa de Pós-Graduação: PROGRAMA DE PÓS-GRADUAÇÃO EM MATEMÁTICA/CCET
• Departamento: DEPARTAMENTO DE MATEMÁTICA/CCET
• País: Brasil
• Palavras-chave em Português: problema dos dois corpos carregados; problema restrito circular dos três corpos carregados; sistemas Hamiltonianos.
• Palavras-chave em Inglês: charged two-body problem; restricted circular problem of three charged bodies; hamiltonian systems.
• Área do conhecimento CNPq: Matemática
• Link de acesso: https://tedebc.ufma.br/jspui/handle/tede/6313

Results on Hamiltonian systems are presented, highlighting that their properties are preserved by symplectic transformations and stability results. Next, the formulation of the n-body problem is addressed, with emphasis on its most well-known classical cases: the two-body problem, whose first integrals are obtained through a symplectic transformation that describes the motion based on the system’s center of mass; and the description of the three-body problem, including its restricted and planar restricted cases. The general problem of charged n-bodies is also addressed, highlighting specific cases: the two-body charged problem, analyzing the behavior for different values of the constant C; and the circular restricted three-body charged problem, where, based on the mass and charge parameters, restrictions on the charge parameters are derived that allow the obtaining of equilibrium solutions (triangular and collinear) and the analysis of their stability.