The three-body problem and equivariant Riemannian geometry

被引：4

作者：

Alvarez-Ramirez, M. ^{[1
]}

Garcia, A. ^{[1
]}

Melendez, J. ^{[1
]}

Reyes-Victoria, J. G. ^{[1
]}

机构：

[1] UAM Iztapalapa, Dept Matemat, San Rafael Atlixco 186, Mexico City 09340, DF, Mexico

来源：

JOURNAL OF MATHEMATICAL PHYSICS | 2017年 / 58卷 / 08期

关键词：

HYPERBOLIC PANTS;

D O I：

10.1063/1.5000075

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We study the planar three-body problem with 1/r(2) potential using the Jacobi-Maupertuis metric, making appropriate reductions by Riemannian submersions. We give a different proof of the Gaussian curvature's sign and the completeness of the space reported by Montgomery [Ergodic Theory Dyn. Syst. 25, 921-947 (2005)]. Moreover, we characterize the geodesics contained in great circles. Published by AIP Publishing.

引用

页数：12

共 7 条

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[3] NO HYPERBOLIC PANTS FOR THE 4-BODY PROBLEM WITH STRONG POTENTIAL
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Montgomery, Richard
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Montgomery, Richard
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[6] Fitting hyperbolic pants to a three-body problem
Montgomery, R
[J]. ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2005, 25 : 921 - 947
[7] The Three-Body Problem and the Shape Sphere
Montgomery, Richard
[J]. AMERICAN MATHEMATICAL MONTHLY, 2015, 122 (04) : 299 - 321

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