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Periodic solutions for planar 2N-body problems

Authors: Shiqing Zhang and Qing Zhou
Journal: Proc. Amer. Math. Soc. 131 (2003), 2161-2170
MSC (2000): Primary 34C25, 34C15, 70F10
Published electronically: November 6, 2002
MathSciNet review: 1963764
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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we study some necessary conditions and sufficient conditions for the nested polygonal solutions of planar 2N-body problems.

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

  • 1. R. Abraham and J. Marsden, Foundations of Mechanics, 2nd ed. Benjamin/Cummings, London, 1978. MR 81e:58025
  • 2. B.Elmabsout, Sur L'existence des certaines configurations d'equilibre relatif dans le probleme des $N$ corps, Celest. Mech. 41(1988), 131-151. MR 89j:70014
  • 3. W. D. MacMillan and W. Bartky, Permanent configurations in the problem of four bodies, Trans. AMS 34 (1932), 838-874.
  • 4. M. Marcus and H. Minc, A survey of matrix theory and matrix inequalities, Allyn and Bacon, Boston, Mass, 1964. MR 29:112
  • 5. R. Moeckel and C. Simó, Bifurcation of spatial central configurations from planar ones, SIAM J. Math. Anal. 26 (1995), 978-998. MR 96d:70015
  • 6. L. M. Perko and E. L. Walter, Regular polygon solutions of the N-body problem, Proc. AMS 94(1985), 301-309. MR 86e:70004
  • 7. Xie Zhifu and Zhang Shiqing, A simpler proof of regular polygon solutions of the N-body problem, Physics Letters A, 277(2000), 156-158.
  • 8. S. Q. Zhang and Q. Zhou, Nested regular polygon solutions for planar 2N-body problems, Preprint, October, 2001.

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Additional Information

Shiqing Zhang
Affiliation: Department of Mathematics, Chongqing University, Chongqing 400044, People’s Republic of China
Address at time of publication: Department of Mathematics, Shanghai Jiaotong University, Shanghai 200030, People’s Republic of China

Qing Zhou
Affiliation: Department of Mathematics, East China Normal University, Shanghai 200062, People’s Republic of China

Keywords: 2N-body problems, nested regular polygon periodic solutions, circulant matrices
Received by editor(s): November 7, 2001
Received by editor(s) in revised form: February 25, 2002
Published electronically: November 6, 2002
Additional Notes: This work was supported by the NSF of China
Communicated by: Carmen C. Chicone
Article copyright: © Copyright 2002 American Mathematical Society