Periodic orbits in the Chermnykh problem

Zeng, Xia; Alfriend, Kyle T.

doi:10.1007/s42064-017-0004-7

Cited by 11 publications

(7 citation statements)

References 28 publications

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“…Kang et al [27] discovered the convergence of a periodic orbit family near asteroids during continuation under proper conditions. Zeng and Alfriend [28] provided a global searching method to find periodic orbits around the dipole model based on the Poincare section.…”

Section: Introductionmentioning

confidence: 99%

Bifurcations of Periodic Orbits in the Gravitational Field of Irregular Bodies: Applications to Bennu and Steins

Liu

Jiang

2022

Aerospace

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We investigate the topological types and bifurcations of periodic orbits in the gravitational field of irregular bodies by the well-known two parameter analysis method. Results show that the topological types of periodic orbits are determined by the locations of these two parameters and that the bifurcation types correspond to their variation paths in the plane. Several new paths corresponding to doubling period bifurcations, tangent bifurcations and Neimark–Sacker bifurcations are discovered. Then, applications in detecting bifurcations of periodic orbits near asteroids 101955 Bennu and 2867 Steins are presented. It is found that tangent bifurcations may occur three times when continuing the vertical orbits near the equilibrium points of 101955 Bennu. The continuation stops as the Jacobi energy reaches a local maximum. However, while continuing the vertical orbits near the equilibrium points of 2867 Steins, the tangent bifurcation and pseudo period-doubling bifurcation occur. The continuation can always go on, and the orbit ultimately becomes nearly circular.

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Section: Introductionmentioning

confidence: 99%

Bifurcations of Periodic Orbits in the Gravitational Field of Irregular Bodies: Applications to Bennu and Steins

Liu

Jiang

2022

Aerospace

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“…Due to the non-spherical shape, the close distance, and the relative orbital and attitude motion of the asteroids, the dynamic environment in binary systems has the chaotic characteristic. A variety of researchers have dealt with the motion near binary asteroids in the past, including analogous equilibrium points [7,8], periodic orbits [9][10][11][12][13][14], resonant orbits [15] and lift-off motion on the surface [16]. Separate periodic orbits and bounded motions have been found based on a non-synchronized model [15,[17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Investigation of Stable Regions of Spacecraft Motion in Binary Asteroid Systems by Terminal Condition Maps

Dong

Jia

2021

J Astronaut Sci

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In this paper, the stable regions of spacecraft motion in binary asteroid systems are studied and applied to design trajectories for exploration missions. Due to the non-spherical shape and the relative motion of small bodies, the motion in a binary asteroid system exhibits chaotic characteristics, which bring difficulties to proximity operations. A terminal condition map is developed to analyze the motion stability, where the initial periapsides of trajectories are classified according to their terminal states, including orbiting the asteroids, impacting on the surface or escaping from the system. The binary asteroid system 66391 Moshup is chosen as the target. The geometry of terminal condition maps is first discussed based on a synchronized model. The stable regions around asteroids are found for both planar and spatial motions, and their evolutions with orbital energy are investigated. Then, a method to trajectory design in binary asteroid systems via terminal condition maps is proposed. Opportunities for ballistic capture and escape are found in the vicinity of the asteroids by matching backward and forward terminal condition maps. Meanwhile, V-assisted periodic orbits, as well as flyby trajectories, can be designed on the basis of the symmetry of maps. Finally, the terminal condition map is applied to discuss the effect of the primary and secondary's mutual motion on the spacecraft motion. This study provides a global picture of the motion stability and makes trajectory design flexible in binary asteroid systems, which can support future binary asteroid exploration missions.

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“…Li et al [33] have investigated the locations and linear stability of equilibrium points as well as periodic orbits around equilibrium points in the vicinity of a rotating dumbbell-shaped body. These simply shaped bodies and potential fields, including the logarithmic gravity field [34], the straight segment [6][8] [13] [35], the solid circular ring [29] [36], the triangular plate and the square plate [14], the homogeneous annulus disk [30][31], the homogeneous cube [32,[37][38][39], the dumbbell-shaped body [33], the classical rotating dipole model [40][41][42], and the dipole segment model [43] are all plane-symmetric. The relative equilibria of spacecrafts in the second degree and order-gravity field [44][45] are different from the equilibria in the above studies.…”

Section: Introductionmentioning

confidence: 99%

“…the classical rotating dipole model [40][41][42], and the dipole segment model [43] are all plane-symmetric. The relative equilibria of spacecrafts in the second degree and order-gravity field [44][45] are different from the equilibria in the above studies.…”

Section: Introductionmentioning

confidence: 99%

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Stability and motion around equilibrium points in the rotating plane-symmetric potential field

et al. 2018

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This study presents a study of equilibrium points, periodic orbits, stabilities, and manifolds in a rotating plane-symmetric potential field. It has been found that the dynamical behaviour near equilibrium points is completely determined by the structure of the submanifolds and subspaces. The non-degenerate equilibrium points are classified into twelve cases. The necessary and sufficient conditions for linearly stable, non-resonant unstable and resonant equilibrium points are established. Furthermore, the results show that a resonant equilibrium point is a Hopf bifurcation point. In addition, if the rotating speed changes, two non-degenerate equilibria may collide and annihilate each other. The theory developed here is lastly applied to two particular cases, motions around a rotating, homogeneous cube and the asteroid 1620 Geographos. We found that the mutual annihilation of equilibrium points occurs as the rotating speed increases, and then the first surface shedding begins near the intersection point of the -x axis and the surface. The results can be applied to planetary science, including the birth and evolution of the minor bodies in the Solar system, the rotational breakup and surface mass shedding of asteroids, etc.

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Periodic orbits in the Chermnykh problem

Cited by 11 publications

References 28 publications

Bifurcations of Periodic Orbits in the Gravitational Field of Irregular Bodies: Applications to Bennu and Steins

Bifurcations of Periodic Orbits in the Gravitational Field of Irregular Bodies: Applications to Bennu and Steins

Investigation of Stable Regions of Spacecraft Motion in Binary Asteroid Systems by Terminal Condition Maps

Stability and motion around equilibrium points in the rotating plane-symmetric potential field

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