This review article aims to give a comprehensive review of periodic orbits in the circular restricted three-body problem(CRTBP),which is a standard ideal model for the Earth-Moon system and is closest to the practical...This review article aims to give a comprehensive review of periodic orbits in the circular restricted three-body problem(CRTBP),which is a standard ideal model for the Earth-Moon system and is closest to the practical mechanical model.It focuses the attention on periodic orbits in the Earth-Moon system.This work is primarily motivated by a series of missions and plans that take advantages of the three-body periodic orbits near the libration points or around two gravitational celestial bodies.Firstly,simple periodic orbits and their classification that is usually considered to be early work before 1970 are summarized,and periodic orbits around Lagrange points,either planar or three-dimensional,are intensively studied during past decades.Subsequently,stability index of a periodic orbit and bifurcation analysis are presented,which demonstrate a guideline to find more periodic orbits inspired by bifurcation signals.Then,the practical techniques for computing a wide range of periodic orbits and associated quasi-periodic orbits,as well as constructing database of periodic orbits by numerical searching techniques are also presented.For those unstable periodic orbits,the station keeping maneuvers are reviewed.Finally,the applications of periodic orbits are presented,including those in practical missions,under consideration,and still in conceptual design stage.This review article has the function of bridging between engineers and researchers,so as to make it more convenient and faster for engineers to understand the complex restricted three-body problem(RTBP).At the same time,it can also provide some technical thinking for general researchers.展开更多
This paper aims to provide further study on the nonlinear modeling and controller design of formation flying spacecraft in deep space missions.First,in the Sun-Earth system,the nonlinear formation dynamics for the cir...This paper aims to provide further study on the nonlinear modeling and controller design of formation flying spacecraft in deep space missions.First,in the Sun-Earth system,the nonlinear formation dynamics for the circular restricted three-body problem(CRTBP)and elliptic restricted three-body problem(ERTBP)are presented.Then,with the Floquet mode method,an impulsive controller is developed to keep the Chief on the desired Halo orbit.Finally,a nonlinear adaptive control scheme based on Nonzero set-point LQR and neural network is proposed to achieve high precision formation maneuver and keeping.The simulation results indicate that the proposed nonlinear control strategy is reasonable as it considers not only the orbit keeping of the Chief,but also the formation modeling inaccuracy.Moreover,the nonlinear adaptive control scheme is effective to improve the control accuracy of the formation keeping.展开更多
Temporary capture efficiency is studied in the framework of the circular restricted three-body problem in two steps.First, a non-uniform distribution of test particles around the secondary's orbit is obtained by f...Temporary capture efficiency is studied in the framework of the circular restricted three-body problem in two steps.First, a non-uniform distribution of test particles around the secondary's orbit is obtained by fully accounting the secondary's gravitational influence. Second, the capture efficiency is computed based on the non-uniform distribution. Several factors influencing the result are discussed. By studying the capture efficiency in the circular restricted three-body problem of different mass ratios, a power-law relation between the capture efficiency(p) and the mass ratio(μ) is established, which is given by p ≈ 0.27 × μ^(0.53), within the range of 3.0035 ×10^(-6)≤ μ ≤ 3.0034 × 10^(-5). Taking the Sun–Earth system as an example, the influence from the orbit eccentricity of the secondary on the non-uniform distribution and the capture efficiency is studied. Our studies find that the secondary's orbit eccentricity has a negative influence on the capture efficiency.展开更多
文摘This review article aims to give a comprehensive review of periodic orbits in the circular restricted three-body problem(CRTBP),which is a standard ideal model for the Earth-Moon system and is closest to the practical mechanical model.It focuses the attention on periodic orbits in the Earth-Moon system.This work is primarily motivated by a series of missions and plans that take advantages of the three-body periodic orbits near the libration points or around two gravitational celestial bodies.Firstly,simple periodic orbits and their classification that is usually considered to be early work before 1970 are summarized,and periodic orbits around Lagrange points,either planar or three-dimensional,are intensively studied during past decades.Subsequently,stability index of a periodic orbit and bifurcation analysis are presented,which demonstrate a guideline to find more periodic orbits inspired by bifurcation signals.Then,the practical techniques for computing a wide range of periodic orbits and associated quasi-periodic orbits,as well as constructing database of periodic orbits by numerical searching techniques are also presented.For those unstable periodic orbits,the station keeping maneuvers are reviewed.Finally,the applications of periodic orbits are presented,including those in practical missions,under consideration,and still in conceptual design stage.This review article has the function of bridging between engineers and researchers,so as to make it more convenient and faster for engineers to understand the complex restricted three-body problem(RTBP).At the same time,it can also provide some technical thinking for general researchers.
文摘This paper aims to provide further study on the nonlinear modeling and controller design of formation flying spacecraft in deep space missions.First,in the Sun-Earth system,the nonlinear formation dynamics for the circular restricted three-body problem(CRTBP)and elliptic restricted three-body problem(ERTBP)are presented.Then,with the Floquet mode method,an impulsive controller is developed to keep the Chief on the desired Halo orbit.Finally,a nonlinear adaptive control scheme based on Nonzero set-point LQR and neural network is proposed to achieve high precision formation maneuver and keeping.The simulation results indicate that the proposed nonlinear control strategy is reasonable as it considers not only the orbit keeping of the Chief,but also the formation modeling inaccuracy.Moreover,the nonlinear adaptive control scheme is effective to improve the control accuracy of the formation keeping.
基金supported by the National Natural Science Foundation of China(No.12233003)the support from Laboratory of Pinghu,Pinghu,China。
文摘Temporary capture efficiency is studied in the framework of the circular restricted three-body problem in two steps.First, a non-uniform distribution of test particles around the secondary's orbit is obtained by fully accounting the secondary's gravitational influence. Second, the capture efficiency is computed based on the non-uniform distribution. Several factors influencing the result are discussed. By studying the capture efficiency in the circular restricted three-body problem of different mass ratios, a power-law relation between the capture efficiency(p) and the mass ratio(μ) is established, which is given by p ≈ 0.27 × μ^(0.53), within the range of 3.0035 ×10^(-6)≤ μ ≤ 3.0034 × 10^(-5). Taking the Sun–Earth system as an example, the influence from the orbit eccentricity of the secondary on the non-uniform distribution and the capture efficiency is studied. Our studies find that the secondary's orbit eccentricity has a negative influence on the capture efficiency.
