论文标题
数百个以高精度计算的图形轨道的新卫星
Hundreds of new satellites of figure-eight orbit computed with high precision
论文作者
论文摘要
著名人物 - 八轨道的卫星（拓扑功能）是平面三体问题的特殊周期解决方案。在本文中，我们根据牛顿方法的连续类似物和高精度算术使用了修改后的牛顿方法，用于对图八轨道的新卫星进行有目的的数值搜索。发现了700多个新卫星，其中包括76个新的线性稳定卫星。新发现的线性稳定的卫星中有7个是编舞。线性稳定性通过对单构矩阵的特征值进行高精度计算来检查。所有发现溶液的初始条件均以150个正确的小数位数给出。
Satellites (topological powers) of the famous figure-eight orbit are special periodic solutions of the planar three-body problem. In this paper we use a modified Newton's method based on the Continuous analog of Newton's method and high precision arithmetic for a purposeful numerical search of new satellites of the figure-eight orbit. Over 700 new satellites are found, including 76 new linearly stable ones. 7 of the newly found linearly stable satellites are choreographies. The linear stability is checked by a high precision computing of the eigenvalues of the monodromy matrices. The initial conditions of all found solutions are given with 150 correct decimal digits.
