航天器v_(∞)转移轨道的模型和解析法  

MODEL AND ANALYTIC METHOD OF SPACECRAFT v∞TRANSFER ORBIT

作　　者：何胜茂[1,2] 高扬[1,2,3] 张皓 王扬鑫 He Shengmao;Gao Yang;Zhang Hao;Wang Yangxin(Technology and Engineering Center for Space Utilization,Chinese Academy of Sciences,Beijing 100094,China;Key Laboratory of Space Utilization,Chinese Academy of Sciences,Beijing 100094,China;School of Aeronautics and Astronautics,University of Chinese Academy of Sciences,Beijing 101408,China)

机构地区：[1]中国科学院空间应用工程与技术中心,北京100094 [2]中国科学院太空应用重点实验室,北京100094 [3]中国科学院大学航空宇航学院,北京101408

出　　处：《力学学报》2024年第10期2987-3001,共15页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家重点研发计划(2022YFC2204700);中国科学院战略性先导科技专项(A类)(XDA30010200)资助项目.

摘　　要：假定A和B是围绕一个引力中心按照开普勒轨道运行的卫星,针对航天器从A出发转移至B的轨道确定问题,文章提出了一个新的模型,称为v∞转移轨道(v∞-transfer-orbit,VTO).VTO选取航天器飞离A的时刻t0和逃逸速度大小v∞作为设计参数,求解抵达B的开普勒轨道.根据A和B运行轨道的空间位置关系,VTO分为A/B异面、A/B共面和A/B重合3种情况,同时存在3类解:General-VTO、Backflip-VTO和Resonant-VTO.文章建立了统一的VTO解析方法,即将航天器抵达B的位置约束分解为轨道约束和时间约束,根据轨道约束推导航天器轨道关于单个变量的解析式,根据时间约束建立该变量的一元方程,从而将原问题转化为一元方程寻根问题.首先,依次针对A/B异面、A/B共面和A/B重合情况构建了General-VTO的一元寻根方程,详细介绍了一元方程的寻根区间,并给出了一种基于三次样条插值的快速寻根算法;然后,构建了Backflip-VTO的一元寻根方程,在分析一元方程函数单调性、极值点和拐点的基础上给出了一元方程寻根区间和寻根方法;之后,构建了Resonant-VTO的直接解析式.最后,给出算例并重点说明VTO多解性.Assuming that there exist the bodies A and B in Keplerian orbits around a single gravitational center and a spacecraft transfers from A to B,a new model called v∞-transfer-orbit(VTO)-problem is proposed for determining the spacecraft’s transfer orbit.In the VTO-problem,the escaping time t0 and the escaping velocity v∞departing from A are selected as the spacecraft’s orbital determination parameters.According to the spatial relative positions between A and B,the VTO-problem is divided into three cases:A/B is nonplanar,A/B is coplanar,and A/B is co-orbital,and there exist three types of solutions:General-VTO,Backflip-VTO and Resonant-VTO.In this paper,a uniform geometric analysis method for solving the VTO-problem is introduced,in which the position constraint of the spacecraft’s arrival at B is decomposed into orbital constraint and time constraint,the spacecraft’s orbital parameters are resolved by a single variable based on the orbital constraint,and an equation referring to this single variable is constructed based on the time constraint.According to the geometric analysis method,the VTO-problem is transformed into a one-variable equationrooting problem.Firstly,the one-variable equation for General-VTO is derived in response to the cases of A/B nonplanar,A/B coplanar,and A/B co-orbital,and the intervals of the variable and an efficient equation-rooting algorithms based on the cubic spline interpolation are elaborated.Secondly,the different one-variable equation-rooting problem for Backflip-VTO is derived,and another set of equation-rooting algorithms are described on the basis of analyzing the equation function properties,such as monotonicity,extreme points and inflection points.Thirdly,the analytic solution is given directly for Resonant-VTO.Finally,examples are given to expound the solution multiplicity of the VTO-problem.

关 键 词：v∞转移轨道 General-VTO Backflip-VTO Resonant-VTO 轨道确定 

分 类 号：V448.2[航空宇航科学与技术—飞行器设计]