Trajectory Design And Stability Analysis For Resonant Orbits In The Circular Restricted Three-Body Problem

When the periods of two or more planetary orbiting a central body exist or approach a rational number relation,such orbits are called resonant orbits.For celestial systems,resonance is the result of long-time evolution between the gravitations of the system.But for the resonant orbits of the spacecraft,they can be designed and have potential application value.The design methods for resonant orbits in the two-body problem and the circular restricted three-body problem(CRTBP)are presented respectively in Earth-Moon system.The effects about two important initial parameters of resonant orbit on the dynamic characteristic and motion are also analyzed.The Kepler energy and the Moon's perturbed gravitational sphere are used as criteria,the initial parameter intervals that can cause instability of the resonant orbits in the CRTBP are obtained,examples are provided to verify the proposed criteria.The stability and bifurcation of resonant orbit families with different resonant ratios in the CRTBP are investigated.The main research contents include:(1)Dynamics model and coordinate system selection: aiming at a series of complex dynamics modeling problem,such as the trajectory design and stability analysis for resonant orbits,the dynamic model and coordinate system involved in this paper are given,and coordinate frame transformations are introduced.(2)Trajectory design and dynamic analysis for resonant orbits: the design methods for resonant orbits in the two-body problem and the CRTBP are presented respectively in Earth-Moon system.Two important initial parameters,eccentricity and initial phase,which affect the dynamic characteristics and motion of the resonant orbit are analyzed,the relative position of resonant orbit with Moon is affected by the initial parameters.The differences of resonance orbits between the two-body problem and the CRTBP are compared.The influence of the moon on the resonant orbit is preliminarily analyzed.(3)Analysis on the initial parameter intervals that can cause resonant orbits to lose steady ratios: based on an analysis of ballistic capture and resonant flyby,the Kepler energy and the Moon's perturbed gravitational sphere are used as criteria to establish connections between the initial parameters and the possible “steady” resonant orbits,the effects of different eccentricities and initial phases on the closest distance between the resonant orbit and the Moon and the Kepler energy with respect the Moon is analyzed,the initial parameter intervals that can cause resonant orbits to lose steady ratios in the CRTBP are obtained.Examples of resonant orbits with 1:2 and 2:1 resonances are provided to verify the proposed criteria.(4)Stability and bifurcation analysis of the resonant orbits: the concept of Monodromy is introduced,take 1:2 and 2:3 resonant orbits as examples,the bifurcation theory is used to find a new type of periodic orbits.Analyze the stability of resonance orbits by stability order and stability index,the range of the unstable resonance orbit and the dimension of invariant manifolds near the unstable resonant orbit are determined.Solve stable and unstable manifolds near the unstable resonant orbits,and realize the visualization of manifolds by Poincare? section in the position-velocity coordinate system,the relationship between manifolds and other structures in phase space can be observed more intuitively.In addition,the examples of 1:3 and 1:4 resonant orbits which are global instability are also presented.