Asteroids and Their Mathematical Methods

Jiang, Yu; Ni, Yaodong; Baoyin, Hexi; Li, Junfeng; Liu, Yongjie

doi:10.3390/math10162897

Cited by 3 publications

(1 citation statement)

References 198 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Period-multiplying bifurcations along the parent periodic orbit family are located. The shooting method is predominantly used in the existing literature for computing periodic orbit families around asteroids [35]. However, it is found in this work that the shooting methods fail to compute period-multiplying bifurcations of periodic orbit families around asteroids accurately.…”

Section: Introductionmentioning

confidence: 94%

Period-Multiplying Bifurcations in the Gravitational Field of Asteroids

Krishna,

Manathara

2024

Aerospace

View full text Add to dashboard Cite

Periodic orbit families around asteroids serve as potential trajectories for space probes, mining facilities, and deep space stations. Bifurcations of these families provide additional candidate orbits for efficient trajectory design around asteroids. While various bifurcations of periodic orbit families around asteroids have been extensively studied, period-multiplying bifurcations have received less attention. This paper focuses on studying period-multiplying bifurcations of periodic orbit families around asteroids. In particular, orbits with periods of approximately 7 and 17 times that of the rotational period of asteroid 216 Kleopatra were computed. The computation of high-period orbits provides insights into the numerical aspects of simulating long-duration trajectories around asteroids. The previous literature uses single-shooting and multiple-shooting methods to compute bifurcations of periodic orbit families around asteroids. Computational difficulties were encountered while using the shooting methods to obtain period-multiplying bifurcations of periodic orbit families around asteroids. This work used the Legendre–Gauss collocation method to compute period-multiplying bifurcations around asteroids. This study recommends the use of collocation methods to obtain long-duration orbits around asteroids when computational difficulties are encountered while using shooting methods.

show abstract

Section: Introductionmentioning

confidence: 94%

Period-Multiplying Bifurcations in the Gravitational Field of Asteroids

Krishna,

Manathara

2024

Aerospace

View full text Add to dashboard Cite

show abstract

Position-attitude coupling guidance and control for asteroid landing with a flexible lander

Yan,

Baoyin

2023

Aerospace Science and Technology

View full text Add to dashboard Cite

The Shape Entropy of Small Bodies

Zhang

et al. 2023

Mathematics

View full text Add to dashboard Cite

The irregular shapes of small bodies usually lead to non-uniform distributions of mass, which makes dynamic behaviors in the vicinities of small bodies different to that of planets. This study proposes shape entropy (SE) as an index that compares the shapes of small bodies and spheres to describe the shape of a small body. The results of derivation and calculation of SE in two-dimensional and three-dimensional cases show that: SE is independent of the size of geometric figures but depends on the shape of the figures; the SE difference between a geometric figure and a circle or a sphere, which is the limit of SE value, reflects the difference between this figure and a circle or a sphere. Therefore, the description of shapes of small bodies, such as near-spherical, ellipsoid, and elongated, can be quantitatively described via a continuous index. Combining SE and the original inertia index, describing the shape of small bodies, can define the shapes of small bodies and provide a reasonably simple metric to describe a complex shape that is applicable to generalized discussion and analysis rather than highly detailed work on a specific, unique, polyhedral model.

show abstract

Asteroids and Their Mathematical Methods

Cited by 3 publications

References 198 publications

Period-Multiplying Bifurcations in the Gravitational Field of Asteroids

Period-Multiplying Bifurcations in the Gravitational Field of Asteroids

Position-attitude coupling guidance and control for asteroid landing with a flexible lander

The Shape Entropy of Small Bodies

Contact Info

Product

Resources

About