Hamilton系统的数值仿真方法研究  

Study on Numerical Simulation Methods of Hamilton Systems

作　　者：何克晶[1] 

机构地区：[1]华南理工大学计算机学院,广东广州510641

出　　处：《计算机仿真》2010年第6期79-82,102,共5页Computer Simulation

摘　　要：针对飞行轨道设计中均为微分方程描述,通过数字仿真方法进行优化,对Hamilton系统的数值积分中的Runge-Kutta-Fehlberg方法、Bulirsch-Stoer方法和Symplectic方法(辛算法)进行了研究比较。通过对各种数值积分的能量误差和动量误差进行对比研究,分析了各种方法在应用于不同的Hamilton系统时的精度和性能。总体而言,辛方法是求解近开普勒轨道的最优方法。在不能使用辛方法时,Bulirsch-Stoer方法是最好的选择。通过对比各种传统算法的应用领域和不足,提出了一种适用于高精度轨道仿真的多层次辛方法(Hierarchical Symplectic Method),并将其用于太阳系的行星轨道仿真。方法将系统分解到不同层次,然后通过结合不同数值积分方法的优点,综合求解,实现快速高精度的行星和卫星轨道仿真。This paper compared the numerical integration methods, including Runge - Kutta - Fehlberg （RKF） method, Bulirsch -Stoer method, and the symplectic method, for the simulation of Hamilton systems. By comparing the energy errors and the momentum errors of different methods, this paper studied the advantages, disadvantages, and application fields of these three methods. Overall, the symplectic method is the best for near - Keplerian problems, and the Bulirsch - Stoer method is preferable to the RKF method when the symplectic method is not applicable. To overcome the difficulties of traditional symplectic method, this paper proposed a Hierarchical Symplectic Method （HSM） for general high - precision orbit simulation. The HSM organizes the system into different levels, and solves the sub - problems at their corresponding levels using the most appropriate integration methods. HSM is efficient and with high accuracy, and its application in integrating the moon＇s orbits demonstrated its applicability.

关 键 词：哈密尔顿系统 多层次辛方法 多体问题 数值方法 

分 类 号：TP391.9[自动化与计算机技术—计算机应用技术]