Numerical search for periodic solutions in the vicinity of the figure-eight orbit: slaloming around singularities on the shape sphere

Milovan ?uvakov

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Numerical search for periodic solutions in the vicinity of the figure-eight orbit: slaloming around singularities on the shape sphere

机译：数值搜索在八字形轨道附近的周期解：围绕形状球上的奇异点激流回旋

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摘要

We present the results of a numerical search for periodic orbits with zero angular momentum in the Newtonian planar three-body problem with equal masses focused on a (narrow) search window bracketing the figure-eight initial conditions. We found eleven solutions that can be described as some power of the "figure-eight" solution in the sense of the topological classification method. One of these solutions, with the seventh power of the "figure-eight", is a choreography. We show numerical evidence of its stability.

机译：我们提出了在牛顿平面三体问题中等角质量为零的牛顿平面三体问题中的周期角动量为零的数值轨道的数值搜索结果，该搜索焦点包围着包含八位数初始条件的（狭窄）搜索窗口。在拓扑分类方法的意义上，我们找到了11个解决方案，这些解决方案可以描述为“数字8”解决方案的某种功能。这些解决方案之一是编排，它具有“八位数”的七次幂。我们显示了其稳定性的数值证据。

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《Celestial Mechanics and Dynamical Astronomy: An international journal of space dynamics》 |2014年第4期|共9页
作者
Milovan ?uvakov;
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正文语种 eng
中图分类天体物理学;
关键词
Three-body problem; Periodic solutions; Choreography; Topological classification; Geometric-algebraic classes;

机译：三体问题周期解编排拓扑分类几何代数类;

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1. Numerical search for periodic solutions in the vicinity of the figure-eight orbit: slaloming around singularities on the shape sphere [J] . Milovan ?uvakov Celestial Mechanics and Dynamical Astronomy: An international journal of space dynamics . 2014,第3a4期

机译：数值搜索在八字形轨道附近的周期解：围绕形状球上的奇异点激流回旋
2. Index and Stability of Symmetric Periodic Orbits in Hamiltonian Systems with Application to Figure-Eight Orbit [J] . Hu Xijun, Sun Shanzhong Communications in Mathematical Physics . 2009,第2期

机译：应用于六八轨道哈密顿系统对称周期轨道的指数及稳定性
3. The existence of periodic solutions of differential equations with pulse action in the vicinity of complex singular points [J] . Samoilenko V G., Sobchuk V V Доκлады Аκадемии науκ Уκраины . 2000,第8期

机译：复奇异点附近带脉冲作用的微分方程周期解的存在
4. A DESIGN OF QUASI-PERIODIC RELATIVE ORBITS USING SINGULAR VALUE STRUCTURE OF ORBITAL STATE TRANSITION MATRIX [C] . Hikaru Uramachi Applications of space technology for humanity . 2010

机译：利用轨道状态转移矩阵的奇异值结构设计准周期相对轨道
5. LOCAL RATES OF MASS TRANSFER FROM SPHERES IN SIMPLE CUBIC PACKING AND A NUMERICAL SOLUTION OF THE NAVIER-STOKES EQUATIONS FOR VISCOUS FLOW PAST ASINGLE SPHERE [D] . RHODES, JOHN MARK -1

机译：简单立方包装中球体的质量转移率以及粘性过去单球体Navier-Stokes方程的数值解
6. Existence of periodic solution for fourth-order generalized neutral p-Laplacian differential equation with attractive and repulsive singularities [O] . Yun Xin, Hongmin Liu -1

机译：具有吸引和排斥奇点的四阶广义中立p-Laplacian微分方程周期解的存在性
7. Numerical Search for Periodic Solutions in the Vicinity of the Figure-Eight Orbit: Slaloming around Singularities on the Shape Sphere [O] . Šuvakov, Milovan 2013

机译：关系中周期解的数值搜索图八轨道：形状球体上的奇点周围的滑坡
8. PART I Recent Work on Families of Periodic Solutions of Ordinary Differential Equations. PART II Singular Solutions of Systems of Real Analytic Equations. PART III The Stromgren-Wintner Principle on the Termination of Families of Periodic Solutions. [R] . Daniel C. Lewis 1959

机译：第一部分关于常微分方程周期解族的近期研究。第二部分实分析方程组的奇异解。第三部分stromgren-Wintner关于终止家庭周期解的原则。

Numerical search for periodic solutions in the vicinity of the figure-eight orbit: slaloming around singularities on the shape sphere

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