遍历理论在航天动力学领域的应用  

The Application of Ergodic Theory in Astrodynamics

作　　者：白雪[1] 徐明[1] 姚闯 BAI Xue;XU Ming;YAO Chuang(Beihang University,Beijing 100191,China;Shanghai Institute of Satellite Engineering,Shanghai 201109,China.)

机构地区：[1]北京航空航天大学,北京100191 [2]上海卫星工程研究所,上海201109

出　　处：《空间控制技术与应用》2018年第4期1-7,15,共8页Aerospace Control and Application

基　　金：国家自然科学基金资助项目(11772024;11432001)~~

摘　　要：系统地研究遍历理论在航天动力学领域的应用,包括椭圆轨道长期覆盖和受晒因子等长期参数的平均化计算.从无摄和J_2项摄动下平均轨道根数的长期和长周期项出发,构造非共振条件下覆盖和受晒因子的测度描述,并证明该测度的不变性;给出相关相空间和相流定义,并证明该相流的保测度性;应用Birkhoff-Khinchin定理将长期覆盖和受晒因子等无限时间的累积问题成功转换为有限空间的二重积分运算.研究结果表明,遍历理论是解决航天动力学领域长期参数统计计算的有力工具.The application of ergodic theory in astrodynamics is systematically studied,including the average calculation of long-term parameters such as the long-term coverage of elliptical orbit and the exposure factor. Based on the long term and long-period term of the average orbital elements with the unperturbed and J_2 perturbation,the measurement description of the coverage and non-eclipse factors under offresonant conditions is constructed,and the invariance of the measure is proved. The correlation phase space and phase flow definition are given,and the preserving measure of the phase flow is proved. Using Birkhoff-Khinchin theorem,the cumulative problem of long-term coverage and non-eclipse factors in infinite time is transformed into a double integral operation in finite space. The research results show that ergodic theory is a powerful tool to solve the long-term parameter calculation in astrodynamics.

关 键 词：遍历算法 Birkhoff-Khinchin定理 长期覆盖 受晒因子 

分 类 号：V476.4[航空宇航科学与技术—飞行器设计]