Spatial twisted central configuration for Newtonian ($ 2N $+1)-body problem

Liang Ding; Jinrong Wang; Jinlong Wei; Liang Ding; Jinrong Wang; Jinlong Wei

doi:10.3934/cam.2024018

Communications in Analysis and Mechanics

2024, Volume 16, Issue 2: 388-415. doi: 10.3934/cam.2024018

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Research article

Spatial twisted central configuration for Newtonian ($ 2N $+1)-body problem

1.
Department of Mathematics, Guizhou University, Guiyang, 550025, P.R. China
2.
School of Data Science and Information Engineering, Guizhou Minzu University, Guiyang, 550025, P.R. China
3.
School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan, 430073, P.R. China

Received: 04 November 2023 Revised: 11 March 2024 Accepted: 10 April 2024 Published: 20 May 2024
70F10, 70F15

For a spatial twisted central configuration of the Newtonian ($ 2N $+1)-body problem where $ 2N $ masses are at the vertices of two paralleled regular $ N $-polygons with distance $ h > 0 $, and the twist angle between the two regular $ N $-polygons is $ 0\leq\theta < 2\pi $, we study the sufficient and necessary conditions for the existence of the spatial twisted central configuration. Additionally, we obtain the uniqueness of the spatial twisted central configuration.
- Newtonian ($ 2N $+1)-body problem,
- spatial central configuration,
- regular $ N $-polygons,
- twist angle
Citation: Liang Ding, Jinrong Wang, Jinlong Wei. Spatial twisted central configuration for Newtonian ($ 2N $+1)-body problem[J]. Communications in Analysis and Mechanics, 2024, 16(2): 388-415. doi: 10.3934/cam.2024018

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Abstract

For a spatial twisted central configuration of the Newtonian ($ 2N $+1)-body problem where $ 2N $ masses are at the vertices of two paralleled regular $ N $-polygons with distance $ h > 0 $, and the twist angle between the two regular $ N $-polygons is $ 0\leq\theta < 2\pi $, we study the sufficient and necessary conditions for the existence of the spatial twisted central configuration. Additionally, we obtain the uniqueness of the spatial twisted central configuration.

References

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