Janković Marija R, Dmitrašinović V
Faculty of Physics, Belgrade University, Studentski Trg 12, 11000 Belgrade, Serbia.
Institute of Physics, Belgrade University, Pregrevica 118, Zemun, P.O. Box 57, 11080 Belgrade, Serbia.
Phys Rev Lett. 2016 Feb 12;116(6):064301. doi: 10.1103/PhysRevLett.116.064301. Epub 2016 Feb 10.
We use 57 recently found topological satellites of Broucke-Hadjidemetriou-Hénon's periodic orbits with values of the topological exponent k ranging from k=3 to k=58 to plot the angular momentum L as a function of the period T, with both L and T rescaled to energy E=-0.5. Upon plotting L(T/k) we find that all our solutions fall on a curve that is virtually indiscernible by the naked eye from the L(T) curve for nonsatellite solutions. The standard deviation of the satellite data from the sixth-order polynomial fit to the progenitor data is σ=0.13. This regularity supports Hénon's 1976 conjecture that the linearly stable Broucke-Hadjidemetriou-Hénon orbits are also perpetually, or Kol'mogorov-Arnol'd-Moser, stable.
我们使用57颗最近发现的布鲁克-哈吉德梅特里乌-亨农周期轨道的拓扑卫星，其拓扑指数k的值范围从k = 3到k = 58，来绘制角动量L作为周期T的函数，其中L和T都重新标度为能量E = -0.5。在绘制L(T/k)时，我们发现所有解都落在一条曲线上，用肉眼几乎无法将其与非卫星解的L(T)曲线区分开来。卫星数据与拟合到原数据的六阶多项式的标准差为σ = 0.13。这种规律性支持了亨农在1976年的猜想，即线性稳定的布鲁克-哈吉德梅特里乌-亨农轨道也是永久稳定的，或者说是科尔莫戈罗夫-阿诺尔德-莫泽稳定的。
