# Dynamics of Equilibrium Points in a Uniformly Rotating Second-Order and Degree Gravitational Field

## Abstract

Using tools such as periodic orbits and invariant manifolds, the global dynamics around equilibrium points (EPs) in a rotating second-order and degree gravitational field are studied. For EPs on the long axis, planar and vertical periodic families are computed, and their stability properties are investigated. Invariant manifolds are also computed, and their relation to the first-order resonances is briefly discussed. For EPs on the short axis, planar and vertical periodic families are studied, with special emphasis on the genealogy of the planar periodic families. Our studies show that the global dynamics around EPs are highly similar to those around libration points in the circular restricted three-body problem, such as spatial halo orbits, invariant manifolds, and the genealogy of planar periodic families.

- Authors:

- School of Astronomy and Space Science, Nanjing University, 210093 (China)

- Publication Date:

- OSTI Identifier:
- 22663467

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Astronomical Journal (Online); Journal Volume: 154; Journal Issue: 1; Other Information: Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ASTEROIDS; EQUILIBRIUM; GRAVITATIONAL FIELDS; INSTABILITY; ORBITS; PERIODICITY; PLANETS; RESONANCE; STABILITY; THREE-BODY PROBLEM

### Citation Formats

```
Feng, Jinglang, and Hou, Xiyun, E-mail: jinglang@nju.edu.cn, E-mail: silence@nju.edu.cn.
```*Dynamics of Equilibrium Points in a Uniformly Rotating Second-Order and Degree Gravitational Field*. United States: N. p., 2017.
Web. doi:10.3847/1538-3881/AA75D0.

```
Feng, Jinglang, & Hou, Xiyun, E-mail: jinglang@nju.edu.cn, E-mail: silence@nju.edu.cn.
```*Dynamics of Equilibrium Points in a Uniformly Rotating Second-Order and Degree Gravitational Field*. United States. doi:10.3847/1538-3881/AA75D0.

```
Feng, Jinglang, and Hou, Xiyun, E-mail: jinglang@nju.edu.cn, E-mail: silence@nju.edu.cn. Sat .
"Dynamics of Equilibrium Points in a Uniformly Rotating Second-Order and Degree Gravitational Field". United States.
doi:10.3847/1538-3881/AA75D0.
```

```
@article{osti_22663467,
```

title = {Dynamics of Equilibrium Points in a Uniformly Rotating Second-Order and Degree Gravitational Field},

author = {Feng, Jinglang and Hou, Xiyun, E-mail: jinglang@nju.edu.cn, E-mail: silence@nju.edu.cn},

abstractNote = {Using tools such as periodic orbits and invariant manifolds, the global dynamics around equilibrium points (EPs) in a rotating second-order and degree gravitational field are studied. For EPs on the long axis, planar and vertical periodic families are computed, and their stability properties are investigated. Invariant manifolds are also computed, and their relation to the first-order resonances is briefly discussed. For EPs on the short axis, planar and vertical periodic families are studied, with special emphasis on the genealogy of the planar periodic families. Our studies show that the global dynamics around EPs are highly similar to those around libration points in the circular restricted three-body problem, such as spatial halo orbits, invariant manifolds, and the genealogy of planar periodic families.},

doi = {10.3847/1538-3881/AA75D0},

journal = {Astronomical Journal (Online)},

number = 1,

volume = 154,

place = {United States},

year = {Sat Jul 01 00:00:00 EDT 2017},

month = {Sat Jul 01 00:00:00 EDT 2017}

}