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

[21] Relative Equilibria in the 3-Dimensional Curved n-Body Problem
Diacu, Florin
MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY, 2014, 228 (1071) : 1 - +
[22] Interaction of bodies in the circular restricted 3-body problem with variable mass
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ASTRONOMY AND COMPUTING, 2023, 42
[23] The analysis of periodic orbits generated by Lagrangian solutions of the restricted three-body problem with non-spherical primaries
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[24] The instability transition for the restricted 3-body problem II. The hodograph eccentricity criterion
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ASTRONOMY & ASTROPHYSICS, 2010, 514
[25] Shapes and Mass Variation Effects of the Bodies in the Generalized Elliptic Restricted 3-Body Problem
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[26] The instability transition for the restricted 3-body problem III. The Lyapunov exponent criterion
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ASTRONOMY & ASTROPHYSICS, 2011, 533
[27] Local minimality properties of circular motions in 1/rα potentials and of the figure-eight solution of the 3-body problem
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[28] Stability of Fixed Points and Associated Relative Equilibria of the 3-Body Problem on S1 and S2
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Manuel Sanchez-Cerritos, Juan
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JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 2018, 30 (01) : 209 - 225
[29] Bifurcation of periodic orbits for the N-body problem, from a nongeometrical family of solutions
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CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY, 2022, 134 (01)
[30] The reduction of the linear stability of elliptic Euler-Moulton solutions of the n-body problem to those of 3-body problems
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Long, Yiming
CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY, 2017, 127 (04) : 397 - 428

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