Equilíbrios e estabilidade linear no problema restrito circular de três corpos

Abstract

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.