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Twisted stacked central configurations for the spatial nine-body problem

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Abstract

In this article, we study the existence of the twisted stacked central configurations for the nine-body problem. More precisely, the position vectors x 1, x 2, x 3, x 4 and x 5 are at the vertices of a square pyramid Σ; the position vectors x 6, x 7, x 8 and x 9 are at the vertices of a square Π; the square (x 1, x 2, x 3, x 4) and the square (x 6, x 7, x 8, x 9) have twisted angle π/4.

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References

  1. Arnold V., Kozlov V., Neishtadt A.: Dynamical Systems, Mathematical Aspects of Classical and Celestial Mechanics. Springer, Berlin (1988)

    Google Scholar 

  2. Wintner A.: The Analytical Foundations of Celestial Mechanics. Princeton University Press, Princeton (1941)

    Google Scholar 

  3. Smale S.: Topology and mechanics \({\amalg}\): The planar n-body problem. Invent. Math. 11, 45–64 (1970)

    Article  MathSciNet  MATH  Google Scholar 

  4. Moeckel R.: On central configurations. Math. Z. 205, 499–517 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  5. Saari D.: On the role and properties of n-body central configurations. Celest. Mech. 21, 9–20 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  6. Albouy A., Kaloshin V.: Finiteness of central configurations of five bodies in the plane. Ann. Math. 176, 535–588 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  7. Hampton M., Santoprete M.: Seven-body central configurations: a family of central configurations in the spatial seven-body problem. Celest. Mech. Dyn. Astron. 99, 293–305 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  8. Llibre J., Mello L.F.: New central configurations for the planar 5-body problem. Celest. Mech. Dynam. Astron. 100, 141–149 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  9. Shi J., Xie Z.: Classification of four-body central configurations with three equal masses. J. Math. Anal. Appl. 363, 512–524 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  10. Ouyang T., Xie Z.: Collinear central configuration in four-body problem. Celest. Mech. Dynam. Astron. 93, 147–166 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  11. Hampton M.: Stacked central configurations: new examples in the planar five-body problem. Nonlinearity 18, 2299–2304 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  12. Llibre J., Mello L.F., Perez-Chavela E.: New stacked central configurations for the planar 5-body problem. Celest. Mech. Dynam. Astron. 110, 45–52 (2011)

    Article  MathSciNet  Google Scholar 

  13. Mello L.F., Chaves F.E., Fernandes A.C., Garcia B.A.: Stacked central configurations for the spatial six-body problem. J. Geom. Phys. 59, 1216–1226 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  14. Zhang S.Q., Zhou Q.: Double pyramidal central configurations. Phys. Lett. A. 281, 240–248 (2001)

    Article  MathSciNet  Google Scholar 

  15. Hampton M., Santoprete M.: Seven-body central configurations: a family of central configurations in the spatial seven-body problem. Celest. Mech. Dynam. Astron. 99, 293–305 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  16. Mello L.F., Fernandes A.C.: Stacked central configurations for the spatial seven-body problem. Qual. Theory Dyn. Syst. 12, 101–114 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  17. Su X., An T.Q.: Twisted stacked central configurations for the spatial seven-body problem. J. Geom. Phys. 70, 164–171 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  18. Albouy A., Fu Y., Sun S.: Symmetry of planar four-body convex central configurations. Proc. R. Soc. A 464, 1355–1365 (2008)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Faculty of Mathematics and Physics, Huaiyin Institute of Technology, Huai’an, 223003, China

    Chunhua Deng & Xia Su

  2. College of Science, Hohai University, Nanjing, 210098, China

    Xia Su

Authors
  1. Chunhua Deng
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  2. Xia Su
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Correspondence to Chunhua Deng.

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Deng, C., Su, X. Twisted stacked central configurations for the spatial nine-body problem. Z. Angew. Math. Phys. 66, 1329–1339 (2015). https://doi.org/10.1007/s00033-014-0466-x

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  • DOI: https://doi.org/10.1007/s00033-014-0466-x

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