关于数值求解天体运动方程的几个问题

本文讨论三个问题：1.在采用各种非辛（Symplectic）的数值积分器积分天体运动方程时，截断误差将引起人为的能量耗散，这一问题是不能用简单地在相应的力模型中加进一个人为的阻力因子而得以解决的，被歪曲的能量（或数值轨道）必须在积分过程的每一步用能量关系来进行校正，此即能量控制方法．2.当摄动加速度涉及到坐标轴的旋转时，如何在各种积分器中采用能量控制方法．3.对于大偏心率轨道，用数值方法求解相应运动方程时，积分步长必须随运动天体与中心天体之间的距离变化而改变，显然，这对所有积分器都是不方便的，特别是多步积分器．本义给出了一种步长均匀化的处理，可以使上述大偏心率轨道积分问题按定步长计算．

SEVERAL PROBLEMS IN THE NUMERICAL INTEGRATION FOR THE EQUATIONS OF CELESTIAL MOTIONS

The following three problems are discussed in this paper. (1) The problem of the artificial dissipation of energy in integrating the quations of motion caused by the local trunction errors cannot be solved with the simple method in which an artificial drag-factor is increased in the corresponding form models. The distorted energy (or numerical orbits) must be dectified using the energy integral or its variational relation at each step of the integration process. (2) It is introduced now to use the "energy control method in numeuical iintegrators", when the disturbing acceleration is related to the rotation of coordinate axis.(3) For an orbit with large eccentricity, the step size of integrating the corresponding equations of motion with numerical methods must be varied with the change of the distance between moving body and Central body. Obviously, thes is not advantageous for all numerical integrators. In thes paper an equalization method of the step size is given.Hence the above problem of larger eccentricity can be solved with a fixed step size in the equalization method.