平面三体问题的高精度琐碎编排数据库

IF 1.9 4区数学 Q1 MATHEMATICS

Numerical Mathematics-Theory Methods and Applications Pub Date : 2022-10-02 DOI:10.48550/arXiv.2210.00594

I. Hristov, R. Hristova, I. Puzynin, T. Puzynina, Z. Sharipov, Z. Tukhliev

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引用次数: 0

摘要

平凡舞蹈是平面三体问题的特殊周期解。在这项工作中，我们使用一种改进的牛顿方法，该方法基于牛顿方法的连续模拟和高精度算法，用于专门的数值搜索新的琐碎编排。作为搜索的结果，我们计算出了一个包含462个这样的轨道的高精度数据库，其中包括397个新轨道。所有解的初始条件和周期都用180位正确的十进制数字给出。108个编舞是线性稳定的，包括99个新编舞。通过对单矩阵特征值的高精度计算，验证了该方法的线性稳定性。

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A database of high precision trivial choreographies for the planar three-body problem

Trivial choreographies are special periodic solutions of the planar three-body problem. In this work we use a modified Newton's method based on the continuous analog of Newton's method and a high precision arithmetic for a specialized numerical search for new trivial choreographies. As a result of the search we computed a high precision database of 462 such orbits, including 397 new ones. The initial conditions and the periods of all found solutions are given with 180 correct decimal digits. 108 of the choreographies are linearly stable, including 99 new ones. The linear stability is tested by a high precision computing of the eigenvalues of the monodromy matrices.

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来源期刊

Numerical Mathematics-Theory Methods and Applications 数学-数学

CiteScore

2.80

自引率

7.70%

发文量

审稿时长

>12 weeks

期刊介绍： Numerical Mathematics: Theory, Methods and Applications (NM-TMA) publishes high-quality original research papers on the construction, analysis and application of numerical methods for solving scientific and engineering problems. Important research and expository papers devoted to the numerical solution of mathematical equations arising in all areas of science and technology are expected. The journal originates from the journal Numerical Mathematics: A Journal of Chinese Universities (English Edition). NM-TMA is a refereed international journal sponsored by Nanjing University and the Ministry of Education of China. As an international journal, NM-TMA is published in a timely fashion in printed and electronic forms.