论文标题
针对平面三体问题的高精度琐碎编排的数据库
A database of high precision trivial choreographies for the planar three-body problem
论文作者
论文摘要
琐碎的编舞是平面三体问题的特殊周期解决方案。在这项工作中，我们根据牛顿方法的连续类似物使用了修改后的牛顿的方法，并使用高精度算术来进行专门的数值搜索，以搜索新的琐碎编舞。由于搜索，我们计算了一个高精度数据库的462个此类轨道，包括397个新轨道。最初的条件和所有发现溶液的周期均以180个正确的小数位数给出。 108个编舞是线性稳定的，其中包括99个新的编舞。线性稳定性通过高精度计算的单构矩阵特征值进行测试。
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.
