Linear stability for some symmetric periodic simultaneous binary collision orbits in the four-body problem

被引：19

作者：

Bakker, Lennard F. ^{[1
]}

Ouyang, Tiancheng ^{[1
]}

Yan, Duokui ^{[2
]}

Simmons, Skyler ^{[1
]}

Roberts, Gareth E. ^{[3
]}

机构：

[1] Brigham Young Univ, Dept Math, Provo, UT 84602 USA

[2] Nankai Univ, Chern Inst Math, Tianjin 300071, Peoples R China

[3] Coll Holy Cross, Dept Math & Comp Sci, Worcester, MA 01610 USA

来源：

CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY | 2010年 / 108卷 / 02期

基金：

美国国家科学基金会;

关键词：

N-body problem; Singular periodic orbits; Stability; Schubart-like orbit; Roberts' method; RECTILINEAR 3-BODY PROBLEM; EXISTENCE; PROOF;

D O I：

10.1007/s10569-010-9298-y

中图分类号：

P1 [天文学];

学科分类号：

0704 ;

摘要：

We apply the analytic-numerical method of Roberts to determine the linear stability of time-reversible periodic simultaneous binary collision orbits in the symmetric collinear four-body problem with masses 1, m, m, 1, and also in a symmetric planar four-body problem with equal masses. In both problems, the assumed symmetries reduce the determination of linear stability to the numerical computation of a single real number. For the collinear problem, this verifies the earlier numerical results of Sweatman for linear stability with respect to collinear and symmetric perturbations.

引用

页码：147 / 164

页数：18

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