Research On Orbit Design And Maintenance Strategy Of Libration Points Based On Invariant Manifold Technique With Two Dominant Motions

Deep space exploration has significant effects and significance for the advancement of science and the development of human civilization,and can help humans to study the origin,evolution and status of the solar system or the universe.The use of libration point technology for deep space exploration can help us achieve these goals.The libration point is the dynamic equilibrium point in the circular restricted three-body problem(CR3BP).It has rich dynamic characteristics and is an excellent place for scientific research on solar activity and cosmic observation.Based on this background,this paper explores the design and keeping of orbits using the invariant manifold technique with two dominant motions method for Halo periodic orbits and Lissajous quasi-periodic orbits near the libration points.First,the coordinate systems involved in this article and the methods of transforming between different coordinate systems are introduced.Based on the analysis of the basic circular restricted three-body model,the dynamic equations of the dimensionless model of the Earth-Moon system and the dimension model of the SunEarth system are given.The foundation of orbit design,stationkeeping and transfer was laid.Secondly,the numerical construction of periodic orbits and quasi-periodic orbits near libration points are introduced,including state transition matrices,differential correction and secondary differential correction.Nonlinear polynomial relations and reduced-order dynamic equations are obtained by the method of invariant manifold technique with two dominant motions.The vibration theory is used to analyze the periodic orbit,and the motion in two directions is selected as the dominant motion.The motion in the other direction is expressed by the expanded polynomial relationship,thus establishing the nonlinear relationship between the three directions.This nonlinear relationship can reflect the dynamic characteristics of periodic motion.And the relationship can be used as a new constraint in track design and stationkeeping at the libration point.Then,the Linstedt-Pincare perturbation method was used to solve the reducedorder dynamic equations,and the third-order approximate analytical solutions of the Halo and Lissajous orbits were obtained.The accurate periodic orbit is obtained by the orbital numerical design method,and the orbit is keeped by using the polynomial relationship as a constraint condition,and the simulation results of the orbit are given.The validity of the proposed method is verified by simulations using the Earth-Moon system,the Sun-Earth system,and a dimensional model with moon perturbation.Finally,the theory and specific calculation method of the invariant manifold orbit related to the periodic orbit around the libration point are discussed.Invariant manifolds have orbit transfer characteristics that do not require energy consumption,which is an important theoretical basis for designing orbit transfer.The orbit design in this paper is divided into two schemes: primary impulse orbit transfer and Hohmann secondary impulse orbit transfer.And the Earth-moon circular restricted three-body problem is used as a typical case for simulation analysis,giving orbital parameters such as time,energy consumption,and orbit transfer time.Through the heteroclinic orbit,a path that can be transferred from the earth to the Halo periodic orbit near the L2 libration point of the earth and the moon is found.