Routing the asteroid surface vehicle with detailed mechanics

Yu, Yang; Baoyin, Hexi

doi:10.1007/s10409-014-0052-7

Cited by 20 publications

(12 citation statements)

References 18 publications

(16 reference statements)

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“…Tardivel et al (2014) derived the impact equation of grains on the surface of an asteroid. Yu and Baoyin (2014) numerically calculated the hopping on the surface of asteroid 1620 Geographos. However, the motion near the surface differs from the remote motion and surface motion.…”

Section: Introductionmentioning

confidence: 99%

“…10x10) Legendre coefficients can model the gravity field of an irregular asteroid. On the other hand, motion near the surface of an asteroid (Yu and Baoyin 2014) does not need to consider the solar gravity, just the high-precision gravity field of irregular asteroid, the coefficient of friction of the surface, and the mascons. The perturbation expansion with low Legendre coefficients is insufficient for the calculation of the motion near the surface of an asteroid, because the higher order terms take many iterations to converge, and even diverge at some points (Elipe and Riaguas 2003).…”

Section: Introductionmentioning

confidence: 99%

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Periodic motion near the surface of asteroids

Jiang

Baoyin

Li³

2015

Astrophys Space Sci

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We are interested in the periodic motion and bifurcations near the surface of an asteroid. The gravity field of an irregular asteroid and the equation of motion of a particle near the surface of an asteroid are studied. The periodic motions around the major body of triple asteroid 216 Kleopatra and the OSIRIS-REx mission target-asteroid 101955 Bennu are discussed. We find that motion near the surface of an irregular asteroid is quite different from the motion near the surface of a homoplastically spheroidal celestial body. The periodic motions around the asteroid 101955 Bennu and 216 Kleopatra indicate that the geometrical shapes of the orbits are probably very sophisticated. There exist both stable periodic motions and unstable periodic motions near the surface of the same irregular asteroid. This periodic motion which is unstable can be resonant or non-resonant. The period-doubling bifurcation and pseudo period-doubling bifurcation of periodic orbits coexist in the same gravity field of the primary of the triple asteroid 216 Kleopatra. It is found that both of the period-doubling bifurcations of periodic orbits and pseudo period-doubling bifurcation of periodic orbits have four different paths. The pseudo period-doubling bifurcation found in the potential field of primary of triple asteroid 216 Kleopatra shows that there exist stable periodic orbits near the primary's equatorial plane, which gives an explanation for the motion stability of the triple asteroid 216 Kleopatra's two moonlets, Alexhelios and Cleoselene. spacecraft or moonlet which is orbiting an irregular asteroid can be modeled by a massless particle (Scheeres 2012;Takahashi et al. 2013;Chanut et al. 2014); if the particle is sufficiently far from the irregular asteroid, the asteroid can be approximately modelled as a sphere and the solar gravitation to the particle should be considered; conversely, if the particle is sufficiently close to the irregular asteroid, the irregular asteroidal gravity field provides the decisive effect on the motion of the particle, and the irregular asteroidal gravity field should be considered and the solar gravitation can be neglected (Borisov and Zakharov 2014;Wang et al. 2014).Recently, a few irregular asteroids were selected to analyze motions around them, including asteroids 4 Vesta (Mondelo et al.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Periodic motion near the surface of asteroids

Jiang

Baoyin

Li³

2015

Astrophys Space Sci

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“…There is only one family of quasi-periodic orbits on the xy plane near each of the equilibrium points E1, E3, E5 and E7, and these quasi-periodic orbits are on the 2-dimensional torus 2 T .…”

Section: Application To the Rotating Homogeneous Cubementioning

confidence: 99%

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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“…Due to the importance of space missions, investigating the dynamic environments near asteroids or comets has gained increasing attention in the past few decades (Delsate 2011;Yu and Baoyin 2014;Gong and Li 2015a, b). Many researchers have conducted studies to discuss the orbital dynamic behaviours near minor bodies.…”

Section: Introductionmentioning

confidence: 99%

Bifurcations of relative equilibrium points during homotopy deformation of asteroids

Liu

Jiang

2021

Celest Mech Dyn Astr

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The bifurcations of relative equilibrium points in the gravitational field of asteroids during homotopy deformation are investigated in this paper. A theorem concerning the continuity of non-degenerate equilibrium points under small variations of parameters and degeneration of equilibrium points after collisions is presented. This can contribute to understanding the bifurcations of the number of equilibrium points. We concentrate on four types of homotopy deformation: from a rotating ellipsoid to a rotating sphere; from 216 Kleopatra to a rotating ellipsoid, a cube and a rectangular parallelepiped. The results show that during the process of deforming a rotating ellipsoid to a sphere, the number of relative equilibria may vary from 1 to 3 to 5. Infinitely many relative equilibria may occur in some critical cases. When deforming 216 Kleopatra to a rotating ellipsoid or a rectangular parallelepiped, the number of relative equilibria changes from 7 to 5 and collisional annihilation of two relative equilibria inside the body occurs, corresponding to a saddle-node bifurcation. The number of relative equilibria changes from 7 to 5 to 9 when 216 Kleopatra is deformed into a rotating cube. Both the saddle-node bifurcation and Hopf bifurcation occur during deformation. Moreover, the positions, eigenvalues, topological types and stability of equilibrium points are studied here.

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Routing the asteroid surface vehicle with detailed mechanics

Cited by 20 publications

References 18 publications

Periodic motion near the surface of asteroids

Periodic motion near the surface of asteroids

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

Bifurcations of relative equilibrium points during homotopy deformation of asteroids

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