Study Of Low-energy Transfer Trajectories In Restricted Multi-body Problem

This dissertation,based on restricted three-body problem and restricted four-body problem,deeply studies the numerical method and the design method of transfer trajectories in deep space exploration.The main contents of this dissertation are as follows:Based on circular restricted three-body problem,the problem of construction of explicit symplectic scheme is investigated.To begin with,by separating original circular restricted three-body problem Hamiltonian function into several systems with nilpotent of degree two,explicit symplectic Euler schemes with respect to different systems with nilpotent of degree two are found.Secondly,all the explicit symplectic Euler schemes are proved to be self-conjugate operators.As a result,explicit composite symplectic schemes are proposed in this paper by combining those Euler schemes.Finally,A numerical simulation study is conducted by using fourth-order explicit composite symplectic scheme and other integrators to calculate the regular orbit and halo orbit in circular restricted three-body problem,and the availability and the superiority of explicit symplectic scheme are verified.The results show that explicit symplectic scheme leads to oscillation of the system energy error in a certain range instead of error dissipation over the long term.Additionally,symplectic algorithms possess lower numerical error than traditional Runge-Kutta methods with the same order.Based on bicircular restricted four-body problem,the geometrical characteristics of time-dependent invariant manifold in four-body system are investigated,and a design method for lunar transfer trajectory using hybrid model combining circular restricted three-body model and bicircular restricted four-body model is presented.To begin with,through using Halo orbit as an initial approximation,a periodic orbit in the bicircular restricted four-body problem is found.Secondly,the time-dependent stable and unstable invariant manifolds are extended from the periodic orbit,and the geometrical characteristics of invariant manifolds in the phase space are investigated.It becomes clear that invariant manifolds also exist in form of tubes,and the tube wall is the separatrix of transit orbits and non-transit orbits.Finally,according to these characteristics,lunar transfer trajectories are built.The result demonstrates the effectiveness and validity of the method.Low-energy lunar trajectories with lunar trajectories are investigated in the Sun-Earth-Moon-Probe bicircular restricted four-body problem.Accordingly,the characteristics of the distribution of trajectories in the phase space are summarized.To begin with,by using time-dependent invariant manifolds,low-energy lunar trajectories with lunar trajectories are sought based on bicircular restricted four-body problem model.Secondly,through treating time as an augmented dimension of the phase space of nonautonomous system,the state space map that reveals the distribution of these lunar trajectories in the phase space is given.As a result,it is become clear that low-energy lunar trajectories exist in families,and every moment of a Sun-Earth-Moon synodic period can be the departure date.Finally,the changing rule of departure impulse,midcourse impulse at Poincare section,transfer duration and system energy of different families are analyzed.Consequently,the impulse optimal family and transfer duration optimal family are obtained respectively.