This paper deals with generation of halo orbits in the three-dimensional photogravitational restricted three-body problem, where the more massive primary is considered as the source of radiation and the smaller primar...This paper deals with generation of halo orbits in the three-dimensional photogravitational restricted three-body problem, where the more massive primary is considered as the source of radiation and the smaller primary is an oblate spheroid with its equatorial plane coincident with the plane of motion. Both the terms due to oblateness of the smaller primary are considered. Numerical as well as analytical solutions are obtained around the Lagrangian point L1, which lies between the primaries, of the Sun-Earth system. A comparison with the real time flight data of SOHO mission is made. Inclusion of oblateness of the smaller primary can improve the accuracy. Due to the effect of radiation pressure and oblateness, the size and the orbital period of the halo orbit around L1 are found to increase.展开更多
The Circular Restricted Three-Body Problem (CRTBP) with more massive primary as an oblate spheroid with its equatorial plane coincident with the plane of motion of the primaries is considered to generate the halo orbi...The Circular Restricted Three-Body Problem (CRTBP) with more massive primary as an oblate spheroid with its equatorial plane coincident with the plane of motion of the primaries is considered to generate the halo orbits around L1 and L2 for the seven satellites (Mimas, Enceladus, Tethys, Dione, Rhea, Titan and Iapetus) of Saturn in the frame work of CRTBP. It is found that the oblateness effect of Saturn on the halo orbits of the satellites closer to Saturn has significant effect compared to the satellites away from it. The halo orbits L1 and L2 are found to move towards Saturn with oblateness.展开更多
We study of halo orbits in the circular restricted three-body problem (CRTBP) with both the primaries as sources of radiation. The positioning of the triangular equilibrium points is discussed in a rotating coordinate...We study of halo orbits in the circular restricted three-body problem (CRTBP) with both the primaries as sources of radiation. The positioning of the triangular equilibrium points is discussed in a rotating coordinate system.展开更多
In this paper,a two-level search method for searching transfer opportunities between interplanetary halo orbits,exploiting the invariant manifolds of the restricted three-body problem,is proposed.In the method,the fir...In this paper,a two-level search method for searching transfer opportunities between interplanetary halo orbits,exploiting the invariant manifolds of the restricted three-body problem,is proposed.In the method,the first-level search procedure is performed under the conditions of the initial time of escape manifold trajectory of the Sun-Earth halo orbit and the terminal time of capture manifold of the target planet fixed,by solving the optimal two-impulsive heliocentric trajectory to connect the two manifold trajectories.The contour map,helpful to the understanding of the global characteristics of the transfer opportunities,taking the initial time of escape manifold and the terminal time of capture manifold as variables,the optimal velocity increment of the first-level search as objective function,is used for the second-level search.Finally,taking the Earth-Mars and Earth-Venus halo to halo transfers for example,the transfer opportunities in 2015-2017 are searched.The results show the effectiveness of the proposed method and reveal the property of quasi-period of transfer opportunities between interplanetary halo orbits.展开更多
This paper discusses the evolutions of invariant manifolds of Halo orbits by low-thrust and lunar gravity.The possibility of applying all these manifolds in designing low-thrust transfer,and the presence of single-imp...This paper discusses the evolutions of invariant manifolds of Halo orbits by low-thrust and lunar gravity.The possibility of applying all these manifolds in designing low-thrust transfer,and the presence of single-impulse trajectories under lunar gravity are also explained.The relationship between invariant manifolds and the altitude of the perigee is investigated using a Poincaré map.Six types of single-impulse transfer trajectories are then attained from the geometry of the invariant manifolds.The evolutions of controlled manifolds are surveyed by the gradient law of Jacobi energy,and the following conclusions are drawn.First,the low thrust(acceleration or deceleration) near the libration point is very inefficient that the spacecraft free-flies along the invariant manifolds.The purpose is to increase its velocity and avoid stagnation near the libration point.Second,all controlled manifolds are captured because they lie inside the boundary of Earth's gravity trap in the configuration space.The evolutions of invariant manifolds under lunar gravity are indicated from the relationship between the lunar phasic angle and the altitude of the perigee.Third and last,most of the manifolds have preserved their topologies in the circular restricted three-body problem.However,the altitudes of the perigee of few manifolds are quite non-continuous,which can be used to generate single-impulse flyby trajectories.展开更多
The dynamics of a rotating tethered satellite system(TSS) in the vicinity of libration points are highly nonlinear and inherently unstable.In order to fulfll the station-keep control of the rotating TSS along halo orb...The dynamics of a rotating tethered satellite system(TSS) in the vicinity of libration points are highly nonlinear and inherently unstable.In order to fulfll the station-keep control of the rotating TSS along halo orbits,a nonlinear output tracking control scheme based on the h–D technique is proposed.Compared with the popular time-variant linear quadratic regulator(LQR) controller,this approach overcomes some limitations such as on-line computations of the algebraic Riccati equation.Besides,the obtained nonlinear suboptimal controller is in a closed form and easy to implement.Numerical simulations show that the TTS trajectories track the periodic reference orbit with low energy consumption in the presence of both tether and initial injection errors.The axis of rotation can keep pointing to an inertial specifc object to fulfll an observation mission.In addition,the thrusts required by the controller are in an acceptable range and can be implemented through some low-thrust propulsion devices.展开更多
本文基于圆型限制性三体模型(Circular Restricted Three Body Problem,CR3BP)研究由地球飞往Halo轨道的转移轨道设计问题,并提出一种定时中途修正的闭环策略。研究Halo轨道稳定性,得到Floquet乘子与Halo轨道幅值的关系,并折衷选择适合...本文基于圆型限制性三体模型(Circular Restricted Three Body Problem,CR3BP)研究由地球飞往Halo轨道的转移轨道设计问题,并提出一种定时中途修正的闭环策略。研究Halo轨道稳定性,得到Floquet乘子与Halo轨道幅值的关系,并折衷选择适合探测任务的Halo轨道幅值。定义不同于以往研究的Poincaré映射用以计算Halo轨道的稳定流形,根据该不变流形的几何性质得到6类单脉冲轨道转移方式。以被文献中忽略的间接轨道转移方式为基础,应用离散线性随机系统的不完全信息最优控制理论给出修正策略,并经由Monte-Carlo模拟给出修正结果的统计信息。展开更多
文摘This paper deals with generation of halo orbits in the three-dimensional photogravitational restricted three-body problem, where the more massive primary is considered as the source of radiation and the smaller primary is an oblate spheroid with its equatorial plane coincident with the plane of motion. Both the terms due to oblateness of the smaller primary are considered. Numerical as well as analytical solutions are obtained around the Lagrangian point L1, which lies between the primaries, of the Sun-Earth system. A comparison with the real time flight data of SOHO mission is made. Inclusion of oblateness of the smaller primary can improve the accuracy. Due to the effect of radiation pressure and oblateness, the size and the orbital period of the halo orbit around L1 are found to increase.
文摘The Circular Restricted Three-Body Problem (CRTBP) with more massive primary as an oblate spheroid with its equatorial plane coincident with the plane of motion of the primaries is considered to generate the halo orbits around L1 and L2 for the seven satellites (Mimas, Enceladus, Tethys, Dione, Rhea, Titan and Iapetus) of Saturn in the frame work of CRTBP. It is found that the oblateness effect of Saturn on the halo orbits of the satellites closer to Saturn has significant effect compared to the satellites away from it. The halo orbits L1 and L2 are found to move towards Saturn with oblateness.
文摘We study of halo orbits in the circular restricted three-body problem (CRTBP) with both the primaries as sources of radiation. The positioning of the triangular equilibrium points is discussed in a rotating coordinate system.
基金supported by the National Basic Research Program of China ("973" Program) (Grant No. 2012CB720000)the National Natural Science Foundation of China (Grant Nos. 10832004 and 11102020)
文摘In this paper,a two-level search method for searching transfer opportunities between interplanetary halo orbits,exploiting the invariant manifolds of the restricted three-body problem,is proposed.In the method,the first-level search procedure is performed under the conditions of the initial time of escape manifold trajectory of the Sun-Earth halo orbit and the terminal time of capture manifold of the target planet fixed,by solving the optimal two-impulsive heliocentric trajectory to connect the two manifold trajectories.The contour map,helpful to the understanding of the global characteristics of the transfer opportunities,taking the initial time of escape manifold and the terminal time of capture manifold as variables,the optimal velocity increment of the first-level search as objective function,is used for the second-level search.Finally,taking the Earth-Mars and Earth-Venus halo to halo transfers for example,the transfer opportunities in 2015-2017 are searched.The results show the effectiveness of the proposed method and reveal the property of quasi-period of transfer opportunities between interplanetary halo orbits.
基金supported by the National Natural Science Foundation of China (Grant No. 11172020)the "Vision" Foundation for the Talents from Ministry of Industry and Information Technology of Chinathe"BlueSky" Foundation for the Talents from Beijing University of Aeronautics and Astronautics
文摘This paper discusses the evolutions of invariant manifolds of Halo orbits by low-thrust and lunar gravity.The possibility of applying all these manifolds in designing low-thrust transfer,and the presence of single-impulse trajectories under lunar gravity are also explained.The relationship between invariant manifolds and the altitude of the perigee is investigated using a Poincaré map.Six types of single-impulse transfer trajectories are then attained from the geometry of the invariant manifolds.The evolutions of controlled manifolds are surveyed by the gradient law of Jacobi energy,and the following conclusions are drawn.First,the low thrust(acceleration or deceleration) near the libration point is very inefficient that the spacecraft free-flies along the invariant manifolds.The purpose is to increase its velocity and avoid stagnation near the libration point.Second,all controlled manifolds are captured because they lie inside the boundary of Earth's gravity trap in the configuration space.The evolutions of invariant manifolds under lunar gravity are indicated from the relationship between the lunar phasic angle and the altitude of the perigee.Third and last,most of the manifolds have preserved their topologies in the circular restricted three-body problem.However,the altitudes of the perigee of few manifolds are quite non-continuous,which can be used to generate single-impulse flyby trajectories.
基金supported by the National Natural Science Foundation of China (No.61174200)
文摘The dynamics of a rotating tethered satellite system(TSS) in the vicinity of libration points are highly nonlinear and inherently unstable.In order to fulfll the station-keep control of the rotating TSS along halo orbits,a nonlinear output tracking control scheme based on the h–D technique is proposed.Compared with the popular time-variant linear quadratic regulator(LQR) controller,this approach overcomes some limitations such as on-line computations of the algebraic Riccati equation.Besides,the obtained nonlinear suboptimal controller is in a closed form and easy to implement.Numerical simulations show that the TTS trajectories track the periodic reference orbit with low energy consumption in the presence of both tether and initial injection errors.The axis of rotation can keep pointing to an inertial specifc object to fulfll an observation mission.In addition,the thrusts required by the controller are in an acceptable range and can be implemented through some low-thrust propulsion devices.
基金National Natural Science Foundation of China (10702003)Innovation Foundation of Beijing University of Aeronautics and Astronautics for Ph.D. Graduates
文摘本文基于圆型限制性三体模型(Circular Restricted Three Body Problem,CR3BP)研究由地球飞往Halo轨道的转移轨道设计问题,并提出一种定时中途修正的闭环策略。研究Halo轨道稳定性,得到Floquet乘子与Halo轨道幅值的关系,并折衷选择适合探测任务的Halo轨道幅值。定义不同于以往研究的Poincaré映射用以计算Halo轨道的稳定流形,根据该不变流形的几何性质得到6类单脉冲轨道转移方式。以被文献中忽略的间接轨道转移方式为基础,应用离散线性随机系统的不完全信息最优控制理论给出修正策略,并经由Monte-Carlo模拟给出修正结果的统计信息。