圆型限制性三体问题相对运动解析研究

针对圆型限制性三体问题共线平动点附近周期/拟周期轨道下的相对运动问题,提出一种新的、通用的解析研究方法。在周期/拟周期轨道近似解析解的基础上,结合微分修正方法,获得了精确的周期/拟周期轨道。对周期/拟周期轨道的单值矩阵进行分析,同时借鉴Floquet理论核心思想,建立了六个相对运动模态,并将相对运动表示为六个相对运动模态的线性组合,获得了相对运动的近似解析解。最后在地-月系统圆型限制性三体问题下,以L1点作为研究对象,分别以Halo轨道、Lissajous轨道和Lyapunov轨道为参考轨道,对相对运动模态和相对运动进行仿真分析,说明了相对运动模态的正确性以及相对运动近似解析解的有效性。     

地-月系平动点及Halo轨道的应用研究

地-月系统的平动点L1点及L2点的Halo轨道在探月工程中有重要的应用价值，可分别用于地月连续通信覆盖和月球背面的探测。由于在地-月系统中太阳的引力不可忽略，特别是在长时间作用以后，其动力学行为与摄动力较小的日-地系统有明显的不同。本文分析了如何利用太阳引力进入地-月系统的L1点及L2点的Halo轨道、以及由Halo轨道进入近月轨道的问题，两者综合起来构成了一条完整的地月低能转移轨道。研究结果对探月轨道设计有一定的参考价值。     

Effects of eccentricity of the reference orbit on multi-tethered satellite formations

The paper discusses the relevance of eccentric reference orbits on the dynamics of a tethered formation, when a massive cable model is included in the analysis of a multi-tethered satellite formation. The formations examined in this study are hub-and-spoke (HAS) and closed-hub-and-spoke (CHAS) configurations for in-plane and Earth-facing spin planes. Stability of the formations is studied by means of numerical simulation, together with the evaluation of the effects of eccentricity on tether elongation, agents relative position, and formation orientation and shape.     

地月系统循环轨道初步设计与特性分析

基于平面圆型限制性三体问题(CR3BP)模型,根据轨道弧以及顺行和逆行特征采用圆锥曲线拼接法设计了5类地月系统周期轨道。以地月系统循环轨道的工程约束为出发点,从轨道周期、近地点高度、近月点高度、交会对接速度、轨道稳定性等方面分析了这5类周期轨道的特性,从中选择了适合地月系统循环轨道任务方案的周期轨道,并对周期轨道进行了优化。该研究为我国未来载人登月工程提供了一种新的思路与理论技术支持。     

Design of transfer trajectories between resonant orbits in the Earth–Moon restricted problem

The application of dynamical systems techniques to mission design has demonstrated that employing invariant manifolds and resonant flybys enables previously unknown trajectory options and potentially reduces the ΔV$\mathrm{\Delta }V$ requirements. In this investigation, planar and three-dimensional resonant orbits are analyzed and cataloged in the Earth–Moon system and the associated invariant manifold structures are computed and visualized with the aid of higher-dimensional Poincaré maps. The relationship between the manifold trajectories associated with multiple resonant orbits is explored through the maps with the objective of constructing resonant transfer arcs. As a result, planar and three-dimensional homoclinic- and heteroclinic-type trajectories between unstable periodic resonant orbits are identified in the Earth–Moon system. To further illustrate the applicability of 2D and 3D resonant orbits in preliminary trajectory design, planar transfers to the vicinity of L₅ and an out-of-plane transfer to a 3D periodic orbit, one that tours the entire Earth–Moon system, are constructed. The design process exploits the invariant manifolds associated with orbits in resonance with the Moon as transfer mechanisms.     

线性相对运动的正切拦截和正切交会轨道研究

针对冲量方向与追踪器速度方向相同的正切轨道问题,用线性相对运动方程研究了正切于初始轨道和正切于目标轨道的共面轨道拦截和轨道交会问题。得到初始和终端时刻的相对速度向量的解析表达式,定义了两个关于目标真近点角的单变量函数,于是正切拦截和正切交会问题等价于这两个函数分别等于零,最后用割线法求解这两个函数的数值解。根据能量最优要求,考虑初始漂移段,分析了一个周期内的最佳初始正切冲量点。仿真结果校验了本文提出的方法。     

基于傅立叶平均法下的连续小推力动力学分析

通过将小推力展开为偏近点角的傅立叶级数,并对高斯摄动方程在一个轨道周期上的平均,将原方程的推力转化为仅由14个傅立叶系数表示的控制变量。仿真计算表明,平均化后的高斯方程使计算量与牛顿积分相比显著减少,且对小推力而言有足够的精度。对利用平均化后的高斯方程计算轨道根数时产生误差的原因进行了研究,并进一步分析小推力的范围和小推力近似表达式对上述误差的影响,为今后小推力下非开普勒轨道动力学分析提供了理论依据和参数。     

逆行地球同步轨道特性探索

为了探索逆行地球同步轨道在主要环境力作用下的轨道特性,给出了适合进行数值仿真的轨道动力学模型,并以先进的RKDP方法进行求解.对所得仿真数据利用求和取平均的方法去除摄动力产生的短周期效应,通过分析去短周期项后的数据揭示出了逆行地球同步轨道的演变特点.     

Dynamical cartography of Earth satellite orbits

We have carried out a numerical investigation of the coupled gravitational and non-gravitational perturbations acting on Earth satellite orbits in an extensive grid, covering the whole circumterrestrial space, using an appropriately modified version of the SWIFT symplectic integrator, which is suitable for long-term ($～$120?years) integrations of the non-averaged equations of motion. Hence, we characterize the long-term dynamics and the phase-space structure of the Earth-orbiter environment, starting from low altitudes ($～$400?km) and going up to the GEO region and beyond. This investigation was done in the framework of the EC-funded “ReDSHIFT” project, with the purpose of enabling the definition of passive debris removal strategies, based on the use of physical mechanisms inherent in the complex dynamics of the problem (i.e., resonances). Accordingly, the complicated interactions among resonances, generated by different perturbing forces (i.e., lunisolar gravity, solar radiation pressure, tesseral harmonics in the geopotential) are accurately depicted in our results, where we can identify the regions of phase space where the motion is regular and long-term stable and regions for which eccentricity growth and even instability due to chaotic behavior can emerge. The results are presented in an “atlas” of dynamical stability maps for different orbital zones, with a particular focus on the (drag-free) range of semimajor axes, where the perturbing effects of the Earth’s oblateness and lunisolar gravity are of comparable order. In some regions, the overlapping of the predominant lunisolar secular and semi-secular resonances furnish a number of interesting disposal hatches at moderate to low eccentricity orbits. All computations were repeated for an increased area-to-mass ratio, simulating the case of a satellite equipped with an on-board, area-augmenting device. We find that this would generally promote the deorbiting process, particularly at the transition region between LEO and MEO. Although direct reentry from very low eccentricities is very unlikely in most cases of interest, we find that a modest “delta-v” ($\mathrm{\Delta }V$) budget would be enough for satellites to be steered into a relatively short-lived resonance and achieve reentry into the Earth’s atmosphere within reasonable timescales ($～$50?years).     

Low-thrust transfer to Backflip orbits

The aim of the work is to design a low-thrust transfer from a Low Earth Orbit to a “useful” periodic orbit in the Earth–Moon Circular Restricted Three Body Model (CR3BP). A useful periodic orbit is here intended as one that moves both in the Earth–Moon plane and out of this plane without any requirements of propellant mass. This is achieved by exploiting a particular class of periodic orbits named Backflip orbits, enabled by the CR3BP. The unique characteristics of this class of periodic solutions allow the design of an almost planar transfer from a geocentric orbit and the use of the Backflip intrinsic characteristics to explore the geospace out of the Earth–Moon plane. The main advantage of this approach is that periodic plane changes can be obtained by performing an almost planar transfer. In order to save propellant mass, so as to increase the scientific payload of the mission, a low-powered transfer is considered. This foresees a thrusting phase to gain energy from a departing circular geocentric orbit and a second thrusting phase to match the state of the target Backflip orbit, separated by an intermediate ballistic phase. This results in a combined application of a low-thrust manoeuvre and of a periodical solution in the CR3BP to realize a new class of missions to explore the Earth–Moon neighbourhoods in a quite inexpensive way. In addition, a low-thrust transit between two different Backflip orbits is analyzed and considered as a possible extension of the proposed mission. Thus, also a Backflip-to-Backflip transfer is addressed where a low-powered probe is able to experience periodic excursions above and below the Earth–Moon plane only performing almost planar and very short transfers.