完备度量空间上的不动点定理

1922年,Banach证明了压缩映射的不动点的存在性。不动点理论对于解决一些实际问题诸如代数方程、微分方程、积分方程中都有应用。B ranc iari[1]提出了完备度量空间上的边值压缩,并证明了边值压缩映射的不动点定理。本文给出了完备度量空间上的三个不动点定理,推广了B ranc iari[1]中的结果,并且举例说明本文的结果是对Banach压缩定理的推广。     

Basic performance of BeiDou-2 navigation satellite system used in LEO satellites precise orbit determination

The visibility for low earth orbit（LEO） satellites provided by the BeiDou-2 system is analyzed and compared with the global positioning system（GPS）. In addition, the spaceborne receivers＇ observations are simulated by the BeiDou satellites broadcast ephemeris and LEO satellites orbits. The precise orbit determination（POD） results show that the along-track component accuracy is much better over the service area than the non-service area, while the accuracy of the other two directions keeps at the same level over different areas. However, the 3-dimensional（3D） accuracy over the two areas shows almost no difference. Only taking into consideration the observation noise and navigation satellite ephemeris errors, the 3D accuracy of the POD is about30 cm. As for the precise relative orbit determination（PROD）, the 3D accuracy is much better over the eastern hemisphere than that of the western hemisphere. The baseline length accuracy is 3.4 mm over the service area, and it is still better than 1 cm over the non-service area. This paper demonstrates that the BeiDou regional constellation could provide global service to LEO satellites for the POD and the PROD. Finally, the benefit of geostationary earth orbit（GEO） satellites is illustrated for POD.     

地月空间NRHO与DRO在月球探测中的应用研究

针对地月系统三体问题低能往返轨道转移在月球探测中的应用研究，结合天体借力飞行技术与混合优化技术，系统分析了不同目标轨道与借力方位对任务飞行时间与燃料消耗等关键参数的影响，给出了往返轨道设计初值的选择策略。针对轨道设计初值猜想问题，首先采用遗传算法与二体Lambert转移快速确定轨迹拼接点初值。在同时考虑近月点与近地点多约束条件下，基于序列二次规划算法与多重打靶法进一步对燃料最优的地月往返轨道进行研究，并推导了约束方程解析梯度提高设计效率。最后分析近月点高度、不同目标轨道的转移时间与燃耗变化特性，对于考虑月球借力的地月空间轨道往返转移设计及参数选取具有重要的参考价值。     

Two-level optimization approach for Mars orbital long-duration,large non-coplanar rendezvous phasing maneuvers

A relative dynamics equation-set based on orbital element differences with J₂ effects is derived, based on which a two-level approach is proposed to optimize the Mars orbital rendezvous phasing with a large difference in the initial ascending node. The up-level problem uses the revolution deviation between the target spacecraft and the chaser as the design variable, and employs a linear search to find the optimum. The low-level problem uses the maneuver revolutions, locations, and impulses as the design variables, and is solved using a hybrid genetic algorithm combined with sequential quadratic programming. To improve the solution accuracy, an iteration method is developed to satisfy the terminal constraints of the absolute numerical integration trajectory. Test cases involving Mars sample return missions with large initial node differences are presented, which show that the relative dynamics, two-level optimization model, and hybrid optimization algorithm are efficient and robust. Compared with previously published results, the total velocity increment has been further reduced by utilizing this proposed approach. It is found that a five-impulse plan requires the least quantity of propellant, and a propellant-optimal minimum rendezvous duration exists for this long-duration, large non-coplanar rendezvous problem.     

Single-event upset in geostationary transfer orbit during solar-activity maximum period measured by the Tsubasa satellite

This paper reports single-event upset (SEU) occurrence related to the space radiation environment in geostationary transfer orbit during solar-activity maximum period measured by the Tsubasa satellite. Most SEUs are measured in the inner radiation belt, indicating that they are mainly caused by trapped protons. Thus, the spatial distribution and the temporal variation of the SEU count correlate well with those of trapped protons. The peak SEU rate appears around L = 1.4. The transition point from SEUs caused by trapped protons to those caused by galactic cosmic rays is around L = 2.6. During the experiment period, increased SEU count was sometimes detected due to solar and geomagnetic events outside the inner radiation belt.     

空间大型结构体组装接口设计及装配性能分析

为满足超大型(公里级)空间结构在轨组装的需求,设计了一种全新的空间大型结构体组装接口并对其装配性能进行了详细的分析。首先,详细设计了一种纯机械式双锁定组装接口。其次,通过建立接口运动学模型,对组装接口的容差性能进行了分析,得出 X 方向容差为14.25 mm, Z 方向容差为15.84 mm,绕 X,Y,Z 三个轴的角度容差分别为5.65°、5.51°和5.34°。最后,对对接接口进行了ADAMS仿真分析,验证了容差分析的正确性,得到了对接机构接触力与静摩擦系数、机械臂推力、碰撞锥角之间的非线性影响关系,为空间对接机构的设计奠定了基础。     

Elliptical formation control based on relative orbit elements

A new set of relative orbit elements（ROEs）is used to derive a new elliptical formation flying model.In-plane and out-of-plane motions can be completely decoupled,which benefts elliptical formation design.The inverse transformation of the state transition matrix is derived to study the relative orbit control strategy.Impulsive feedback control laws are developed for both in-plane and out-of-plane relative motions.Control of in-plane and out-of-plane relative motions can be completely decoupled using the ROE-based feedback control law.A tangential impulsive control method is proposed to study the relationship of fuel consumption and maneuvering positions.An optimal analytical along-track impulsive control strategy is then derived.Different typical orbit maneuvers,including formation establishment,reconfguration,long-distance maneuvers,and formation keeping,are taken as examples to demonstrate the performance of the proposed control laws.The effects of relative measurement errors are also considered to validate the high accuracy of the proposed control method.     

基于hp自适应伪谱法的可调推力最优离轨研究

根据不同最优化指标要求,利用hp自适应伪谱法,对比分析了固定推力和可调推力制动离轨时的参数变化情况.通过研究发现,以燃料最省为优化指标,采用可调推力制动时,飞行器过渡段飞行时间更长,燃料消耗相对较小;而在时间最短指标要求下,可调推力制动虽消耗大量燃料,但能大大缩短过渡段飞行时间,有利于航天器在执行紧急任务时的快速返回.     

Fast low-energy halo-to-halo transfers between Sun–planet systems

In this paper, the problem of fast low-energy halo-to-halo transfers between Sun–planet systems is discussed under ephemeris constraints. According to the structure of an invariant manifold, employing an invariant manifold and planetary gravity assist to save fuel consumption is analyzed from the view of orbital energy. Then, a pseudo-manifold is introduced to replace the invariant manifold in such a way that more transfer opportunities are allowed. Fast escape and capture can be achieved along the pseudo-manifold. Furthermore, a global searching method that is based on patched-models is proposed to find an appropriate transfer trajectory. In this searching method, the trajectory is divided into several segments that can be designed under simple dynamical models, and an analytical algorithm is developed for connecting the segments. Earth–Mars and Earth–Venus halo-to-halo transfers are designed to demonstrate the proposed approach. Numerical results show that the transfers that combine the pseudo-manifolds and planetary gravity assist can offer significant fuel consumption and flight time savings over traditional transfer schemes.