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A note on the two nested regular polygonal central configurations


Authors: Zhiqiang Wang and Fengying Li
Journal: Proc. Amer. Math. Soc. 143 (2015), 4817-4822
MSC (2010): Primary 34A34, 70F10, 70F15
DOI: https://doi.org/10.1090/S0002-9939-2015-12618-4
Published electronically: April 2, 2015
MathSciNet review: 3391039
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Abstract: This paper is concerned with nested polygonal central configurations for the Newtonian 2n-body problem. We show that when two nested regular n-polygons ($ n\geq 3$) with masses located at the vertices form a central configuration where the twisted angle $ \theta $ is zero, then the value of masses in each separate polygon must be equal.


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Additional Information

Zhiqiang Wang
Affiliation: Department of mathematics, Sichuan University, Chengdu, Sichuan 610064, People’s Republic of China
Email: Wangzhiqiang0213@gmail.com

Fengying Li
Affiliation: School of Economics and Mathematics, Southwestern University of Finance and Economics, Chengdu, Sichuan, 611130, People’s Republic of China
Email: lify0308@163.com

DOI: https://doi.org/10.1090/S0002-9939-2015-12618-4
Keywords: Newtonian N-body problems, nested regular polygonal central configurations, circulant matrices
Received by editor(s): July 31, 2014
Received by editor(s) in revised form: August 24, 2014
Published electronically: April 2, 2015
Additional Notes: Fengying Li is the corresponding author.
Communicated by: Yingfei Yi
Article copyright: © Copyright 2015 American Mathematical Society

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