Numerical study of the linear and nonlinear dynamics near l1 and l2 points in the earth-moon system

Studies of the restricted three-body problem can help in understanding the dynamics of three-body interactions in the solar system. The Lagrangian points have important applications in astronautics, since they are equilibrium points of the equation of motion and very good candidates to locate a satellite or a space station. Zero velocity curves were plotted for constant values of C. The curves were used to define areas of the Lagrange points of the Circular Restricted Three-Body Problem. The equations of motion were linearized to find the eigenvectors and eigenvalues. We computing the eigenvalues to investigate the stability. The invariant manifold structures of the collinear libration points for the spatial restricted three-body problem provide the framework for understanding complex dynamical phenomena from a geometric point of view. In order to generate a trajectory around the Earth, Moon and Earth-Moon system, the two-dimensional nonlinear equations of motion were numerically integrated.