Geometric characterization for the least Lagrangian action ofn-body problems |
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| Authors: | Shiqing Zhang Qing Zhou |
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| Affiliation: | 1. Department of Mathematics, Chongqing University, 400044, Chongqing, China
2. Department of Mathematics, East China Normal University, 200062, Shanghai, China
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| Abstract: | For n-body problems with quasihomogeneous potentials in ?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. |
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