Periodic Orbits Design based on the Center Manifold Theory in the Circular Restricted Three-Body Problem

摘要

This paper proposes a design method for a three-dimensional periodic orbit in the vicinity of a collinear libration point in the circular restricted three-body problem. The proposed method consists of two steps: the orbit design step and the correction step. The first step is based on the center manifold theorem and systematically provides a quasi-periodic orbit parametrized by a single parameter vector. In the second step, the parameter vector in the first step is corrected by using the state transition matrix. The advantage of the proposed method is that it requires neither an initial guess for a periodic orbit in advance nor complex algebraic manipulations, hence it is easy to implement in computers. Two types of correction equations are derived and verified in numerical simulations.