限制性三体问题中显式辛格式的构造  

Construction of explicit symplectic scheme in restricted three-body problem

作　　者：韦炳威 李银山[1] 

机构地区：[1]河北工业大学机械工程学院,天津300130

出　　处：《河北工业大学学报》2017年第1期40-47,共8页Journal of Hebei University of Technology

基　　金：国家自然科学基金(10632040)

摘　　要：针对圆型限制性三体问题(CR3BP)研究了显式辛积分格式的构造问题.首先通过把CR3BP对应的哈密顿函数拆分成若干个二阶幂零哈密顿系统,得到每个二阶幂零哈密顿系统对应的显式欧拉格式.然后证明了每个显式欧拉格式都是自共轭算子,针对这样的特点提出了一种由这些欧拉格式复合得到的显式组合辛格式.最后利用本文提出的显式辛格式与其他积分器求解了CR3BP下的一般轨道和Halo轨道,验证了显式辛格式有效性和优越性.研究发现显式辛格式能长时间保持系统能量误差在一定范围内波动不会出现发散,且计算精度高于同阶的非辛算法.The problem of construction of explicit symplectic scheme is investigated based on circular restricted three-body problem（CR3BP）. To begin with, by separating original CR3BP Hamiltonian function into several systems with nilpotent of degree two, explicit symplectic Euler schemes with respect to different systems with nilpotent of degree two are found. Secondly, all the explicit symplectic Euler schemes are proved to be self-conjugate operators. As a result, explicit composite symplectic schemes are proposed in the paper by combining those Euler schemes. Finally, a numerical simulation study is conducted by using fourth-order explicit composite symplectic scheme and other integrators to calculate the regular orbit and halo orbit in CR3BP, and the availability and superiority of explicit symplectic scheme are verified. The results show that explicit symplectic scheme leads to oscillation of the system energy error in a certain range instead of error dissipation over the long term. Moreover, symplectic algorithms possess higher numerical accuracy than traditional Runge-Kutta methods with the same order.

关 键 词：辛几何算法 限制性三体问题 哈密顿系统 组合格式 

分 类 号：P132.2[天文地球—天体力学] P138.2[天文地球—天文学]