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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 | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)

  • [1] Florin Diacu, Polygonal homographic orbits of the curved $ n$-body problem, Trans. Amer. Math. Soc. 364 (2012), no. 5, 2783-2802. MR 2888228, https://doi.org/10.1090/S0002-9947-2011-05558-3
  • [2] Wei Li and Zhiqiang Wang, The relationships between regular polygon central configurations and masses for Newtonian $ N$-body problems, Phys. Lett. A 377 (2013), no. 31-33, 1875-1880. MR 3065527, https://doi.org/10.1016/j.physleta.2013.05.044
  • [3] Marvin Marcus and Henryk Minc, A survey of matrix theory and matrix inequalities, Dover Publications, Inc., New York, 1992. Reprint of the 1969 edition. MR 1215484
  • [4] Richard Moeckel and Carles Simó, Bifurcation of spatial central configurations from planar ones, SIAM J. Math. Anal. 26 (1995), no. 4, 978-998. MR 1338370 (96d:70015), https://doi.org/10.1137/S0036141093248414
  • [5] L. M. Perko and E. L. Walter, Regular polygon solutions of the $ N$-body problem, Proc. Amer. Math. Soc. 94 (1985), no. 2, 301-309. MR 784183 (86e:70004), https://doi.org/10.2307/2045395
  • [6] Zhifu Xie and Shiqing Zhang, A simpler proof of regular polygon solutions of the $ N$-body problem, Phys. Lett. A 277 (2000), no. 3, 156-158. MR 1808487 (2002b:70019), https://doi.org/10.1016/S0375-9601(00)00698-8
  • [7] Xiang Yu and Shiqing Zhang, Twisted angles for central configurations formed by two twisted regular polygons, J. Differential Equations 253 (2012), no. 7, 2106-2122. MR 2946965, https://doi.org/10.1016/j.jde.2012.06.017
  • [8] Shiqing Zhang and Qing Zhou, Periodic solutions for planar $ 2N$-body problems, Proc. Amer. Math. Soc. 131 (2003), no. 7, 2161-2170. MR 1963764 (2003m:70040), https://doi.org/10.1090/S0002-9939-02-06795-3

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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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