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.     

基于解析梯度的经典Lambert问题迭代求解方法

针对现有求解模型复杂、收敛速度慢等问题,在将经典Lambert转移问题转化为超越方程的基础上,提出一种基于解析梯度的Lambert问题迭代求解算法。选择转移轨道的真近点角为迭代变量,导出转移时间关于真近点角的解析梯度,构造一种基于解析梯度的牛顿迭代算法,降低了算法计算复杂度。理论分析表明该算法具有二阶以上的收敛速度。依据偏心率向量与转移轨道形状的关系,通过几何方法分析得到转移轨道在初始位置处的速度约束条件,推导转移轨道真近点角的最大值和最小值的解析表达式,并采用线性插值方法确定迭代初值,进一步提高了迭代算法的收敛速度。数学仿真结果表明在各种转移条件下算法均能快速收敛,采用所给出的初值选取方法初值确定精度高,进而能够加快收敛速度,而与较割线法相比较收敛速度快、计算量小,验证了所提出算法的有效性。     

严格随机正则(3,s)-SAT模型及其相变现象

研究变元和文字出现次数受限制的规则3-SAT问题,提出了一种严格随机正则（3,s）-SAT问题,并给出了该问题的实例产生模型--SRR模型。结合一阶矩方法和生成函数展开项系数的渐近近似技术,证明了严格随机正则（3,s）-SAT问题相变点的上界,即当变元规模N较大且变元出现次数s>11时,严格随机正则（3,s）-SAT实例是高概率不可满足的。实验结果表明：由SRR模型所生成的随机实例中,当N>60且s>11时,所有的（3,s）-SAT实例均是不可满足的,而当N>150且s<11时,所有的（3,s）-SAT实例均是可满足的,即严格随机正则（3,s）-SAT实例的相变点位于s=11处,且在s=11处（子句变元比为11/3）的严格随机正则（3,s）-SAT实例,比在相变点（子句变元比）4.267处同规模的均匀随机3-SAT实例更难求解,因此,SRR模型可以很方便地在s=11处构造难解的随机3-SAT实例。     

“嫦娥二号”卫星拓展试验轨道计算中心天体的选取

飞行器的星历积分不可避免涉及中心天体的选取问题。“嫦娥二号”卫星在拓展试验期间处于弱引力区,文章针对拓展试验期间的轨道状态,从受摄运动二体问题角度分析得出适宜选取太阳作为中心天体。进而结合真实力模型情况,使用行星星历表计算行星产生的摄动力,从理论上推导得出在忽略小天体摄动的前提下,由于摄动天体同时对中心天体和飞行器产生摄动作用,以地球为中心天体产生的摄动力类似于潮汐力,而以太阳为中心天体则不然,因而更适宜选取地球作为中心天体计算轨道运动问题     

Two 3-D multi-cascade co-design inverse methods based on streamline curvature approach and Clebsch formulation for single-stage centrifugal compressors

Two strategies extended the single-cascade methods from a compressible three-dimensional inverse method for radial and mixed flow turbomachines to two three-dimensional multi-cascade co-design methods for single-stage centrifugal compressors.These two three-dimensional methods and a typical quasi-three-dimensional streamline curvature through-flow inverse method were employed to design the same subsonic high-speed single-stage centrifugal compressors.The compressor performances were simulated by a commercial Reynolds averaged Navier-Stokes (RANS) equations solver.The studies show that two three-dimensional co-design methods are reasonable and feasible.It was found that:firstly the blade camber angle designed by the three-dimensional methods was larger than that designed by the quasi-three-dimensional method;and secondly with regard to two three-dimensional methods with different boundary conditions,the co-design result differences between the diffusers were small,but those between the deswirlers were relatively large.      

非线性热传导逆问题的表面热流辨识方法

当材料的热物性参数随温度变化时,其内部的热传导方程是一非线性偏微分方程,对应的热传导逆问题称为非线性热传导逆问题。本文建立了非线性热传导逆问题的两种表面热流辨识方法:顺序函数法和共轭梯度法,介绍了这两种辨识方法的基本思想和具体算法推导,并针对典型算例进行了仿真辨识,结果表明:两种辨识方法虽然在算法构造、计算效率方面存在一定的差异,但都能给出较好的辨识结果,并且算法受测量噪声的影响较小,具有较好的鲁棒性。     

Gravitationally bound geoengineering dust shade at the inner Lagrange point

This paper presents a novel method of space-based geoengineering which uses the mass of a captured near Earth asteroid to gravitationally anchor a cloud of unprocessed dust in the vicinity of the _L1${\mathrm{L}}_1$ position to reduce the level of solar insolation at Earth. It has subsequently been shown that a cloud contained within the zero-velocity curve of the largest near Earth asteroid, Ganymed, can lead to an insolation reduction of 6.58% on Earth, which is significantly larger than the 1.7% required to offset a 2 °C increase in mean global temperature. The masses of the next largest near Earth asteroids are found to be too small to achieve the required level of insolation reduction, however, they are significant enough to be used as part of a portfolio of geoengineering schemes.     

高超声速飞行器上升段最优制导间接法研究

高超声速飞行器的机身－推进一体化设计使得气动和推进之间存在强非线性耦合,本文针对高超声速飞行器的特点,提出了求解最优上升轨迹的一种可行方案。在零侧滑角和力矩瞬间平衡假设下对上升段飞行问题进行最优建模,将质量引入为状态量,以最省燃料为指标,以推力方向为最优控制量,根据极大值原理推导一阶最优条件。为数值求解两点边值问题,以解析解作为初始猜想,应用经典的有限差分方法和改进的牛顿法,在满足攻角过程约束下,通过同伦算法迭代求解最优轨迹。仿真在给定的初始约束和终端约束下进行,结果表明该制导算法能够实现对高超声速飞行器上升轨迹的优化,以参考面积为同伦参数的迭代方法,能够保证算法的收敛性和快速性。
     

由三个向量对构造三对角对称矩阵

文章讨论利用给定的三个向量对构造不可约三对角矩阵、Jacobi矩阵和负Jacobi矩阵的反问题.在求解方法中,将已知的-些关系式等价地转化为线性方程组,利用线性方程组有解的条件,得到了所研究问题有惟一解的充要条件,并给出了数值算法和例子.     

径流与斜流涡轮设计的通流反问题方法

自主发展了径流及斜流涡轮的准三维流线曲率法通流设计程序,应用该程序给出了一项500 N推力级微型涡喷发动机斜流涡轮的气动设计和叶片造型.通过计算流体力学检验和整体叶轮强度检验,该微型斜流涡轮超过了预定的设计指标.为实现径流涡轮和斜流涡轮设计反问题的统一,流线曲率法的S_2,m流面准径向平衡方程是沿流线方向m和流线的准法线方向口写出,该系统也可用于轴流涡轮的设计.采用了在所有计算站上的"全可控涡法"进行气动设计.