Geometric characterization for the least Lagrangian action of n-body problems

Shiqing Zhang; Qing Zhou

doi:10.1007/BF02872278

Geometric characterization for the least Lagrangian action of n-body problems

Shiqing Zhang^*
, Qing Zhou

^*Corresponding author for this work

School of Mathematical Sciences

Chongqing University

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

For n-body problems with quasihomogeneous potentials in ℝ^k (2[n/2] ≤ k) we prove that the minimum of the Lagrangian action integral defined on the zero mean loop space is exactly the circles with center at the origin and the configuration of the n-bodies is always a regular n - 1 simplex with fixed side length.

Original language	English
Pages (from-to)	15-20
Number of pages	6
Journal	Science in China, Series A: Mathematics
Volume	44
Issue number	1
DOIs	https://doi.org/10.1007/BF02872278
State	Published - Jan 2001

Keywords

Homographic solutions
Lagrangian action integral
n-body problems

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10.1007/BF02872278

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abstract = "For n-body problems with quasihomogeneous potentials in ℝk (2[n/2] ≤ k) we prove that the minimum of the Lagrangian action integral defined on the zero mean loop space is exactly the circles with center at the origin and the configuration of the n-bodies is always a regular n - 1 simplex with fixed side length.",

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AB - For n-body problems with quasihomogeneous potentials in ℝk (2[n/2] ≤ k) we prove that the minimum of the Lagrangian action integral defined on the zero mean loop space is exactly the circles with center at the origin and the configuration of the n-bodies is always a regular n - 1 simplex with fixed side length.

KW - Homographic solutions

KW - Lagrangian action integral

KW - n-body problems

UR - https://www.scopus.com/pages/publications/0035043109

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DO - 10.1007/BF02872278

M3 - 文章

AN - SCOPUS:0035043109

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JO - Science in China, Series A: Mathematics

JF - Science in China, Series A: Mathematics

IS - 1

ER -

Geometric characterization for the least Lagrangian action of n-body problems

Abstract

Keywords

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