A continuum of periodic solutions to the planar four-body problem with two pairs of equal masses

Tiancheng Ouyang; Zhifu Xie

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A continuum of periodic solutions to the planar four-body problem with two pairs of equal masses

机译：连续的周期性解决方案与两对等群众的平面四体问题

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Abstract

In this paper, we apply the variational method with Structural Prescribed Boundary Conditions (SPBC) to prove the existence of periodic and quasi-periodic solutions for the planar four-body problem with two pairs of equal massesm1=m3andm2=m4. A pathq(t)on[0,T]satisfies the SPBC if the boundariesq(0)∈Aand

机译：摘要在本文中，我们将变分方法应用于结构规定边界条件（SPBC）证明两对等质量平面四体问题周期解和拟周期解的存在性http://www.w3.org/1998/Math/MathML“altimg=“si1。（mml:mi>mml:m>mml:m>mml:mmml:mi>mml:ml:ml:m>mml:mmml:mmml:姆姆l:m国有>mml:m>mml:ml:m>mml:ml:m>mml:ml:ml:m>mml:m>mml:m>q（t）on[，T]如果边界http://www.w3.org/1998/Math/MathML“altimg=“si5。gif“display=“inline”overflow=“scroll”>q（0）∈A和

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来源
《Journal of Differential Equations》 |2018年第7期|共31页
作者
Tiancheng Ouyang; Zhifu Xie;
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作者单位

Department of Mathematics Brigham Young University;

Department of Mathematics The University of Southern Mississippi;

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原文格式 PDF
正文语种 eng
中图分类微分方程、积分方程;
关键词
Variational method; Choreographic periodic solutions; Structural Prescribed Boundary Conditions (SPBC); Stability; Central configurations; n-body problem;

机译：变分方法;编排周期解决方案;结构规定的边界条件（SPBC）;稳定性;中央配置;正文问题;

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4. COEXISTENCE OF THE CHAOS AND THE PERIODIC SOLUTIONS IN PLANAR FLUID FLOWS [J] . 袁晓凤, 郭瑞海应用数学和力学：英文版 . 1991,第012期
5. A continuum of periodic solutions to the planar four-body problem with two pairs of equal masses [J] . Tiancheng Ouyang, Zhifu Xie Journal of Differential Equations . 2018,第7期

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A continuum of periodic solutions to the planar four-body problem with two pairs of equal masses

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