Extending Nacozy’s Approach to Correct All Orbital Elements for Each of Multiple Bodies
Extending Nacozy’s Approach to Correct All Orbital Elements for Each of Multiple Bodies
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DOI：
10.1086/591730
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发表时间：
2008-11
期刊：
影响因子：
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通讯作者：
D. Ma;Xin Wu;S. Zhong
中科院分区：
文献类型：
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作者：
D. Ma;Xin Wu;S. Zhong
对于行星动力学中的n体问题的每个对象，除平均异常之外的轨道元素直接由五个独立的慢变量或拟积分决定，其中包括开普勒能量、角动量矢量的三个分量和拉普拉斯矢量的z分量。平均异常取决于开普勒能量指定的平均运动。减少这些准积分在每个积分步骤中的积分误差意味着在很大程度上提高所有元素的精度。因此，我们将这些量的积分不变关系的参考值作为误差的控制源，然后对纳科齐的流形校正思想进行扩展。如果所采用的基本积分器能够为所考虑的稳定源提供必要的精度，则该技术在校正所有元素的显式有效性方面几乎与福岛的线性变换方法相同。尤其是在显着抑制高偏心率下数值误差的增长方面发挥着更为重要的作用。
For each object of an n-body problem in planetary dynamics, orbital elements except the mean anomaly are directly determined by five independently slow-varying quantities or quasi-integrals, which include the Keplerian energy, the three components of the angular momentum vector, and the z-component of the Laplace vector. The mean anomaly depends on the mean motion specified by the Keplerian energy. Decreasing integration errors of these quasi-integrals at every integration step means improving the accuracy of all the elements to a great extent. Because of this, we take reference values of these quantities in terms of the integral invariant relations as control sources of the errors and then give an extension of Nacozy’s idea of manifold correction. The technique is almost the same as the linear transformation method of Fukushima in its explicit validity of correcting all elements, if the adopted basic integrators can give a necessary precision to the stabilizing sources considered. Especially it plays a more important role in significantly suppressing the growth of numerical errors in high eccentricities.