变分离散化开普勒问题中的数值进动
Numerical precession in variational discretizations of the Kepler problem
AI总结：
本文基于变分离散化方法，研究开普勒问题中椭圆轨道的进动现象，通过隐式中点法则和斯托默-弗莱特方法的扰动分析，提出新的数值积分器以提高计算精度。
摘要：
变分离散化方法在开普勒问题中的数值进动研究中，通过修改方程的拉格朗日结构和诺特定理的扰动版本，提供了隐式中点法则（MP）和斯托默-弗莱特方法（SV）的进动估计。基于这些估计，构造了在开普勒问题上表现显著优于MP和SV的新数值积分器。
英文摘要：
Kepler's first law states that the orbit of a point mass with negative energy in a classical gravitational potential is an ellipse with one of its foci at the gravitational center. In numerical simulations of this system one often observes a slight precession of the ellipse around the gravitational center. Using the Lagrangian structure of modified equations and a perturbative version of Noether's theorem, we provide leading order estimates of this precession for the implicit MidPoint rule (MP) and the Störmer-Verlet method (SV). Based on those estimates we construct some new numerical integrators that perform significantly better than MP and SV on the Kepler problem.
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