Efficient Orbit Integration by Linear Transformation for Consistency of Kepler Energy, Full Laplace Integral, and Angular Momentum Vector
Efficient Orbit Integration by Linear Transformation for Consistency of Kepler Energy, Full Laplace Integral, and Angular Momentum Vector
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DOI：
10.1086/420808
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发表时间：
2004-06
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影响因子：
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通讯作者：
T. Fukushima
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文献类型：
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作者：
T. Fukushima
通过采用一般的线性变换作为流形修正的方法，我们改进了我们的对偶标度法，数值积分拟开普勒轨道。新方法在每一步积分中调整积分位置和速度，以精确满足开普勒能量、角动量矢量和全拉普拉斯矢量的关系。在无摄动的情况下，除了在历元的平均经度，它随时间线性增长，在所有的轨道要素的积分误差减少到整个积分的机器的水平。对于摄动轨道，位置积分误差小于以前的流形修正方法。由于其广泛的适用性是不变的，额外的计算成本同样可以忽略不计，我们建议新的方法作为最好的我们的方法的流形校正。
By adopting a general linear transformation as the method of manifold correction, we modify our dual scaling method to integrate quasi-Keplerian orbits numerically. The new method adjusts the integrated position and velocity at each integration step in order to exactly satisfy the relations for the Kepler energy, angular momentum vector, and the full Laplace vector. In the case of no perturbation, the integration errors in all the orbital elements except the mean longitude at the epoch, which grows linearly with time, are reduced to the level of the machine epsilon throughout the integration. For perturbed orbits, the integration errors in position are smaller than with the previous methods of manifold correction. Since its wide applicability is unchanged and the cost of additional computation is similarly negligible, we recommend the new method as the best of our methods of manifold correction.