Theory Of Periodic And Quasi-Periodic Orbits Surrounding The Collinear Libration Points

There are plenty of families of periodic orbits surrounding the collinear libration points in Circular Restricted Three-body Problem(CRTBP) model. Compared with the periodic orbits of restricted two-body problem, the orbits surrounding the collinear libration points have distinct differences in space configuration, constructing methods and stability. These orbits provide more extensive orbit selection for deep space exploration. It refines our understanding of orbital mechanics to research them.This paper firstly introduces the families of periodic orbits and quasi-periodic orbits surrounding the collinear points in CRTBP, and also the methods to construct them and to analyze their stability and bifurcation. Then orbits in CRTBP model and real model of Earth-Moon system are discussed respectively. Main work is shown as follows:1. The third-order analytical solution of periodic and quasi-periodic orbits within a small area surrounding the three collinear libration points is constructed, using Lindstedt-Poincare series method. The numerical iterative method for obtaining the exact period and quasi-period orbits is introduced, and also the numerical exact quasi-period orbits with maneuvers and constraints.2. Monodromy matrix is introduced to analyze the stability and bifurcation of the period orbit using its eigenvalues, and to calculate the whole family of periodic orbits,the family's bifurcations and stable and unstable manifolds surrouding orbits using its eigenvectors.3. The space configuration, linear stability and bifurcations of the families of vertical Lyapunnov, planar Lyapunov and Halo orbits, as well as the stable and unstable manifolds surrounding the orbits are discussed in Earth-Moon CRTBP model and the real Earth-Moon model repectively. The evolutive relation of Lyapunov, Halo and Lissajous families is found out using bifurcations of the three families.4. The searching of periodic and quasi-periodic orbits in the real Earth-Moon model supplyed by JPL ephemeris, using Target Shooting method. It is found that, as part of the orbits get closer to Moon or Earth, the orbits in CRTBP model get more and more unstable, and the orbits in real model needs more and more maneuvers to maintain. This is because the gravitation on the orbits gets greater and changes more fastly. 5. Compared with the orbits in the restricted two-body problem model, the orbits in the CRTBP model have distinct differences in space configuration, constructing methods and stability. There are two types of possible applications--the target orbits and the transfer trajectories.