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New Classes of Spatial Central Configurations for N + N + 2-Body Problem

Author

Listed:
  • Liu Xuefei
  • Zhang Chuntao
  • Luo Jianmei
  • Zhang Gan

Abstract

Under arbitrary masses, in this paper, we discuss the existence of new families of spatial central configurations for the N + N + 2-body problem, ð ‘ â‰¥ 2 . We study some necessary conditions and sufficient conditions for a families of spatial double pyramidical central configurations (d.p.c.c.), where 2 N bodies are at the vertices of a nested regular N -gons Γ 1 ∪ Γ 2 , and the other two bodies are symmetrically located on the straight line that is perpendicular to the plane that contains Γ 1 ∪ Γ 2 and passes through the geometric center of Γ 1 ∪ Γ 2 . We prove that if the bodies are in a d.p.c.c., then the masses on each N -gon are equal, and the other two are also equal. And also we prove the existence and uniqueness of the central configurations for any given ratios of masses.

Suggested Citation

  • Liu Xuefei & Zhang Chuntao & Luo Jianmei & Zhang Gan, 2012. "New Classes of Spatial Central Configurations for N + N + 2-Body Problem," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-19, May.
    • Handle: RePEc:hin:jnlaaa:948356
    DOI: 10.1155/2012/948356
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