论文标题
一种用于准轻巧轨道的新校正方法
A new correction method for quasi-Keplerian orbits
论文作者
论文摘要
一个纯的两体问题具有七个积分，包括开普勒能量，拉普拉斯矢量和角动量矢量。但是，其中只有五个是独立的。当保留了五个独立积分时，从理论观点中自然保留了另外两个相关积分。但是它们可能不是数值计算观点。因此，我们使用七个比例因素来调整集成位置和速度，以使调整后的解决方案严格满足七个约束。注意到两个依赖积分的存在，我们采用了牛顿迭代方法与奇异值分解相结合来计算这些因素。该校正方案可以应用于太阳系中的两体和N体问题。在这种情况下，每个行星的七个量随时间变化。通过整合这些数量的整体关系和运动方程，可以将更准确的值给出七个缓慢变化的量。他们应该对调整后的解决方案感到满意。数值测试表明，新方法可以显着降低所有轨道元件的数值误差的快速增长。
A pure two-body problem has seven integrals including the Kepler energy, the Laplace vector, and the angular momentum vector. However, only five of them are independent. When the five independent integrals are preserved, the two other dependent integrals are naturally preserved from a theoretical viewpoint; but they may not be either from a numerical computational viewpoint. Because of this, we use seven scale factors to adjust the integrated positions and velocities so that the adjusted solutions strictly satisfy the seven constraints. Noticing the existence of the two dependent integrals, we adopt the Newton iterative method combined with the singular value decomposition to calculate these factors. This correction scheme can be applied to perturbed two-body and N-body problems in the solar system. In this case, the seven quantities of each planet slowly vary with time. More accurate values can be given to the seven slowly-varying quantities by integrating the integral invariant relations of these quantities and the equations of motion. They should be satisfied with the adjusted solutions. Numerical tests show that the new method can significantly reduce the rapid growth of numerical errors of all orbital elements.
