Bifurcations of the Lagrangian orbits from the classical to the curved 3-body problem

被引：8

作者：

Diacu, Florin ^{[1
,2
]}

机构：

[1] Univ Victoria, Pacific Inst Math Sci, Victoria, BC V8W 2Y2, Canada

[2] Univ Victoria, Dept Math & Stat, Victoria, BC V8W 2Y2, Canada

来源：

JOURNAL OF MATHEMATICAL PHYSICS | 2016年 / 57卷 / 11期

关键词：

N-BODY PROBLEM; POLYGONAL HOMOGRAPHIC ORBITS; RELATIVE EQUILIBRIA; INTRINSIC APPROACH; SPACES; EXISTENCE; STABILITY;

D O I：

10.1063/1.4967443

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We consider the 3-body problem of celestial mechanics in Euclidean, elliptic, and hyperbolic spaces and study how the Lagrangian (equilateral) relative equilibria bifurcate when the Gaussian curvature varies. We thus prove the existence of new classes of orbits. In particular, we find some families of isosceles triangles, which occur in elliptic space. Published by AIP Publishing.

引用

页数：20

共 42 条

[1] All the Lagrangian relative equilibria of the curved 3-body problem have equal masses
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Popa, Sergiu
JOURNAL OF MATHEMATICAL PHYSICS, 2014, 55 (11)
[2] RECTANGULAR ORBITS OF THE CURVED 4-BODY PROBLEM
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[3] PERIODIC ORBITS FOR THE PERTURBED PLANAR CIRCULAR RESTRICTED 3-BODY PROBLEM
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[4] The Classical N-body Problem in the Context of Curved Space
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[5] Periodic orbits and bifurcations in the Sitnikov four-body problem
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[6] Periodic orbits and bifurcations in the Sitnikov four-body problem
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[8] Hyperbolicity of elliptic Lagrangian orbits in the planar three body problem
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[9] BIFURCATIONS OF SEPARATRICES IN THE AVERAGED PLANAR GENERAL 3-BODY PROBLEM AT 1ST-ORDER RESONANCE
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[10] EULERIAN RELATIVE EQUILIBRIA OF THE CURVED 3-BODY PROBLEMS IN S2
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