几何代数及其在摄动Kepler问题中的应用  

Geometric algebra and its application in perturbing Kepler problem

作　　者：方茹[1] 曹喜滨[2] 张锦绣[2] 

机构地区：[1]哈尔滨工业大学数学系,哈尔滨150001 [2]哈尔滨工业大学卫星技术研究所,哈尔滨150001

出　　处：《哈尔滨工业大学学报》2008年第2期282-286,共5页Journal of Harbin Institute of Technology

基　　金：国家安全重大基础研究(5131201-4)资助项目

摘　　要：为避免卫星轨道摄动分析过程中多种代数系统繁琐的相互转换,创新性地引入几何代数系统,在统一的代数框架内研究摄动开普勒问题.利用几何代数体系中的位置空间与旋量空间之间的转换关系,将摄动Kep ler方程转化为线性、正则的旋量方程(简称KS方程),并给出Kep ler旋量方程的解.最后,通过与传统方法比较,说明几何代数这种新工具在卫星轨道运动中应用的独特优势.In the course of the satellite orbit perturbing analysis, geometric algebra system was introduced innovationally to avoid trivial transformations of various algebra systems and the perturbing Kepler problem was studied in the unified algebra frame. Based on the transformation between position space and spinor space in geometric algebra system, the perturbing Kepler equation was transformed to a linear and regular form （also called Kustaanheimo-Stiefel equation or KS equation）. Moreover, the Kepler problem was solved in term of a quaternion-valued function. Compared with traditional methods, it shows special advantages of geometric algebra in motion of satellite orbit.

关 键 词：几何代数 Kepler方程 旋量 旋转 

分 类 号：V412.4[航空宇航科学与技术—航空宇航推进理论与工程]