The low-energy lunar landing trajectory design using the invariant manifolds of restricted three-body problem is studied. Considering angle between the ecliptic plane and lunar orbit plane, the four-body problem of su...The low-energy lunar landing trajectory design using the invariant manifolds of restricted three-body problem is studied. Considering angle between the ecliptic plane and lunar orbit plane, the four-body problem of sun-earth-moon-spacecraft is divided into two three-body problems, the sun-earth-spacecraft in the ecliptic plane and the earth-moon-spacecraft in the lunar orbit plane. Using the orbit maneuver at the place where the two planes and the invariant manifolds intersect, a general method to design low energy lunar landing trajectory is given. It is found that this method can save the energy about 20% compared to the traditional Hohmann transfer trajectory. The mechanism that the method can save energy is investigated in the point of view of energy and the expression of the amount of energy saved is given. In addition, some rules of selecting parameters with respect to orbit design are provided. The method of energy analysis in the paper can be extended to energy analysis in deep space orbit design.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-i...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 invafiant manifolds and the altitude of the perigee is investigated using a Poincare 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 con- trolled manifolds are captured because they lie inside the boundary of Eatlh＇s gravity trap in the configuration space. The evo- lutions 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
Using the theory of invariant manifolds, we give local expressions of the stable and unstable manifolds for normally hyperbolic invariant tori, and study the existence of transverse orbits heteroclinic to hyperbolic i...Using the theory of invariant manifolds, we give local expressions of the stable and unstable manifolds for normally hyperbolic invariant tori, and study the existence of transverse orbits heteroclinic to hyperbolic invariant tori. These extend and improve the corresponding results obtained in [3-5].展开更多
The interest in the periodic orbits of the restricted three-body problem continues to grow for their significant practical application.This paper focuses on the interplanetary transfers between periodic orbits of two ...The interest in the periodic orbits of the restricted three-body problem continues to grow for their significant practical application.This paper focuses on the interplanetary transfers between periodic orbits of two different three-body systems,whose invariant manifolds have no intersection in phase space.A novel design method is proposed to obtain the optimal transfer employing the invariant manifolds and planetary gravity assist.The periapsis Poincare map is used to analyze the periapsides of invariant manifolds.On the basis of hyperbola approximation,the impulses performed on the periapsis of invariant manifolds are calculated with a simple iterative algorithm.The propellant-efficient escape and capture trajectories can be found by comparing the impulses magnitudes corresponding to different invariant manifolds,which can provide the appropriate initial guess for optimization.Further,the trajectory design is formulated as an unconstrained optimization problem under the perturbed restricted three-body model.An efficient algorithm combining simplex method and differential correction is adopted to obtain the optimal solution.The validity of the proposed approach is demonstrated through several interplanetary low energy transfer trajectories.展开更多
By considering the spacecraft as an extended,rigid body with a prior known attitude instead of a point mass,the attitude-restricted orbital dynamics can improve the precision of the classical point-mass orbital dynami...By considering the spacecraft as an extended,rigid body with a prior known attitude instead of a point mass,the attitude-restricted orbital dynamics can improve the precision of the classical point-mass orbital dynamics in close proximity to an asteroid,because it includes the perturbation caused by the gravitational orbit–attitude coupling of the spacecraft(GOACP).The GOACP is defined as the difference between the gravity acting on a non-spherical,extended body(the real case of a spacecraft)and the gravity acting on a point mass(the approximation of a spacecraft in classical orbital dynamics).Inplane equilibrium points that are within the principal planes of the asteroid have been investigated for the attitude-restricted orbital dynamics in previous studies,including equatorial and in-plane non-equatorial equilibrium points.In this study,out-of-plane equilibrium points outside the principal planes of the asteroid were examined.Out-ofplane equilibrium points cannot exist in the classical point-mass orbital dynamics but do exist in the attitude-restricted orbital dynamics owing to the effects of the GOACP.The previously investigated in-plane equilibrium points and the out-of-plane ones examined in this study provide a complete map of the equilibrium points in close proximity to an asteroid with the GOACP.Equatorial and in-plane non-equatorial equilibrium points have extended the longitude and latitude ranges of the classical equilibrium points without the GOACP,respectively,while the out-of-plane ones examined in the present study extend both the longitude and latitude ranges.Additionally,the invariant manifolds of out-of-plane equilibrium points were calculated,and the results indicated that the attitude of spacecraft significantly affects the invariant manifolds.In practice,these equilibrium points can provide natural hovering positions for operations in proximity to asteroids,and their invariant manifolds can be used for transfers to or from the equilibrium points.展开更多
Investigation of new orbit geometries exhibits a very attractive behavior for a spacecraft to monitor space weather coming from the Sun. Several orbit transfer mechanisms are analyzed as potential alternatives to moni...Investigation of new orbit geometries exhibits a very attractive behavior for a spacecraft to monitor space weather coming from the Sun. Several orbit transfer mechanisms are analyzed as potential alternatives to monitor solar activity such as a sub-solar orbit or quasi-satellite orbit and short and long heteroclinic and homoclinic connections between the triangular points L4 and L5 and the collinear point L3 of the CRTBP （circular restricted three-body problem） in the Sun-Earth system. These trajectories could serve as channels through where material can be transported from L5 to L3 by performing small maneuvers at the departure of the Trojan orbit. The size of these maneuvers at L5 is between 299 m/s and 730 m/s depending on the transfer time of the trajectory and does not need any deterministic maneuvers at L3. Our results suggest that material may also be transported from the Trojan orbits to quasi-satellite orbits or even displaced quasi-satellite orbits.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.10672084 and 10602027)
文摘The low-energy lunar landing trajectory design using the invariant manifolds of restricted three-body problem is studied. Considering angle between the ecliptic plane and lunar orbit plane, the four-body problem of sun-earth-moon-spacecraft is divided into two three-body problems, the sun-earth-spacecraft in the ecliptic plane and the earth-moon-spacecraft in the lunar orbit plane. Using the orbit maneuver at the place where the two planes and the invariant manifolds intersect, a general method to design low energy lunar landing trajectory is given. It is found that this method can save the energy about 20% compared to the traditional Hohmann transfer trajectory. The mechanism that the method can save energy is investigated in the point of view of energy and the expression of the amount of energy saved is given. In addition, some rules of selecting parameters with respect to orbit design are provided. The method of energy analysis in the paper can be extended to energy analysis in deep space orbit design.
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 invafiant manifolds and the altitude of the perigee is investigated using a Poincare 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 con- trolled manifolds are captured because they lie inside the boundary of Eatlh＇s gravity trap in the configuration space. The evo- lutions 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 Shanghai Natural Science Foundation.
文摘Using the theory of invariant manifolds, we give local expressions of the stable and unstable manifolds for normally hyperbolic invariant tori, and study the existence of transverse orbits heteroclinic to hyperbolic invariant tori. These extend and improve the corresponding results obtained in [3-5].
基金supported by the National Basic Research Program of China ("973" Program) (Grant No. 2012CB720000)the National Natural Science Foundation of China (Grant No. 11102021)Foundation of Science and Technology on Space Intelligent Control Laboratory
文摘The interest in the periodic orbits of the restricted three-body problem continues to grow for their significant practical application.This paper focuses on the interplanetary transfers between periodic orbits of two different three-body systems,whose invariant manifolds have no intersection in phase space.A novel design method is proposed to obtain the optimal transfer employing the invariant manifolds and planetary gravity assist.The periapsis Poincare map is used to analyze the periapsides of invariant manifolds.On the basis of hyperbola approximation,the impulses performed on the periapsis of invariant manifolds are calculated with a simple iterative algorithm.The propellant-efficient escape and capture trajectories can be found by comparing the impulses magnitudes corresponding to different invariant manifolds,which can provide the appropriate initial guess for optimization.Further,the trajectory design is formulated as an unconstrained optimization problem under the perturbed restricted three-body model.An efficient algorithm combining simplex method and differential correction is adopted to obtain the optimal solution.The validity of the proposed approach is demonstrated through several interplanetary low energy transfer trajectories.
基金supported by the National Natural Science Foundation of China under Grant Nos.11602009,11432001 and 11872007the Fundamental Research Funds for the Central Universities.
文摘By considering the spacecraft as an extended,rigid body with a prior known attitude instead of a point mass,the attitude-restricted orbital dynamics can improve the precision of the classical point-mass orbital dynamics in close proximity to an asteroid,because it includes the perturbation caused by the gravitational orbit–attitude coupling of the spacecraft(GOACP).The GOACP is defined as the difference between the gravity acting on a non-spherical,extended body(the real case of a spacecraft)and the gravity acting on a point mass(the approximation of a spacecraft in classical orbital dynamics).Inplane equilibrium points that are within the principal planes of the asteroid have been investigated for the attitude-restricted orbital dynamics in previous studies,including equatorial and in-plane non-equatorial equilibrium points.In this study,out-of-plane equilibrium points outside the principal planes of the asteroid were examined.Out-ofplane equilibrium points cannot exist in the classical point-mass orbital dynamics but do exist in the attitude-restricted orbital dynamics owing to the effects of the GOACP.The previously investigated in-plane equilibrium points and the out-of-plane ones examined in this study provide a complete map of the equilibrium points in close proximity to an asteroid with the GOACP.Equatorial and in-plane non-equatorial equilibrium points have extended the longitude and latitude ranges of the classical equilibrium points without the GOACP,respectively,while the out-of-plane ones examined in the present study extend both the longitude and latitude ranges.Additionally,the invariant manifolds of out-of-plane equilibrium points were calculated,and the results indicated that the attitude of spacecraft significantly affects the invariant manifolds.In practice,these equilibrium points can provide natural hovering positions for operations in proximity to asteroids,and their invariant manifolds can be used for transfers to or from the equilibrium points.
文摘Investigation of new orbit geometries exhibits a very attractive behavior for a spacecraft to monitor space weather coming from the Sun. Several orbit transfer mechanisms are analyzed as potential alternatives to monitor solar activity such as a sub-solar orbit or quasi-satellite orbit and short and long heteroclinic and homoclinic connections between the triangular points L4 and L5 and the collinear point L3 of the CRTBP （circular restricted three-body problem） in the Sun-Earth system. These trajectories could serve as channels through where material can be transported from L5 to L3 by performing small maneuvers at the departure of the Trojan orbit. The size of these maneuvers at L5 is between 299 m/s and 730 m/s depending on the transfer time of the trajectory and does not need any deterministic maneuvers at L3. Our results suggest that material may also be transported from the Trojan orbits to quasi-satellite orbits or even displaced quasi-satellite orbits.
