求解最优月球软着陆轨道的隐式打靶法

基于间接法思想推导出一种隐式打靶法对月球软着陆轨道优化问题进行了研究。建立月球软着陆轨道归一化系统模型,利用庞特亚金极大值原理将月球软着陆轨道优化问题转化为满足最优必要条件的两点边值问题（TPBVP）,采用一种新的时间变量使两点边值问题的终端时刻固定,同时将终端时刻看作状态变量并引入终端时刻的哈密尔顿函数值作为隐式终端条件,提出一种隐式打靶法对含有隐式终端条件的两点边值问题进行迭代求解,从而得出燃料消耗最优的月球软着陆轨道。仿真结果表明,与直接法和混合法相比,隐式打靶法优化精度高,收敛速度快,实现了月球软着陆过程燃料消耗最优。同时应用隐式打靶法求解不同发动机推力值的最优月球软着陆问题,得到燃料消耗最小的最优推重比,可为月面着陆器下降级发动机选型提供参考。     

廊坊市中小企业电子商务存在的问题及对策研究

随着全球信息化水平的提高,越来越多企业清晰认识到电子商务的价值所在,而传统企业为了能在电子商务这个虚拟的更为广阔的数字市场空间展示更多的产品、提供更个性化的服务、寻求更大的发展,也纷纷加入其中。电子商务的实施对中小企业本身和整个国民经济都具有极其重要的战略意义,廊坊的中小企业电子商务也逐步朝着国际化、主流化、移动化的趋势发展。逐步加快电子商务的应用和建设,大力发展中小企业电子商务对于加快廊坊市国民经济和社会信息化进程,以信息化带动工业化,以工业化促进信息化,走新型工业化道路,实现全面建设小康社会的宏伟目标具有十分重要的意义。     

从地球到日-火系平动点轨道的转移

平动点轨道特殊的空间位置及动力学特征,使其在深空探测中具有重要的应用。以日-火系平动点轨道(Lissajous与Halo轨道)任务为目标,结合平动点轨道的不变流形理论,研究了小推力转移问题。首先给出了圆型限制性三体动力学模型下平动点附近不变流形(稳定和不稳定流形)高阶分析解以及相应的计算实例。接着以流形分析解为基础,建立了初始小推力轨道优化模型,并利用改进的协作进化算法求解初始小推力轨道。最后将初始轨道离散,采用多点打靶法将最优控制问题转化为参数优化问题,并用序列二次规划方法(SQP)求解。仿真结果证明轨道设计方法的有效性。     

Earth–Moon low energy trajectory optimization in the real system

The problem of the Earth–Moon low energy trajectory optimization in the real system (the model defined by the JPL ephemeris DE405) is considered in this paper. First, this problem is investigated in the model of circular restricted three-body problem, since the fuel consumption is closely related to the Jacobi integral of the transfer trajectory, a method based on Jacobi integral is proposed and eight optimal trajectories are obtained. These optimal trajectories provide initial information (the flight time and the braking velocity impulse) to search the optimal low energy trajectories in the real system through optimization techniques. Considering the merit and drawback of particle swarm optimization and differential evolution algorithm in solving the space trajectory problem, an improved cooperative evolutionary algorithm is put forward. Result shows that the low energy trajectories in the real system are more fuel-efficient than the corresponding ones under the circular restricted three-body problem.     

单站观测卫星初轨计算中的初值方法

研究了用单个观测站粗略确定低轨卫星轨道的问题, 建立了在时间轴上拓展的测量方程组, 并着重讨论了其中的初值问题; 给出了两种基于线性变换的初值方法, 并对其性能做了比较。实验结果证明： 这些方法能给出一个确定的、实用的初值, 大大减少了初轨计算的计算量, 并使得算法收敛更加有保障, 在工程实用方面比传统的猜测方法具有较大优势。     

激光燃速仪的燃烧室流场分析计算

 Numerical method of flow field of laser servo-controlled strand window bomb was studied and discussed. Stream function and vorticity method of axisymmetric, steady, incompressible flow field was also studied and discussed. Axisymmetric finite difference stream function-vorticity equations on interior points and the points near oblique boundary were derived. Boundary conditions were given and initial interative field was offered before calculation. Cross-bidirectional scanning method was used for increasing parameter transmission rate and relaxation method which could increase convergent stability was applied. At last, the flow field of laser servo-controlled strand window bomb was shown, including motion patterns and vorticity flow scatter diagrams. The solutions were in concordance to the solutions by Mills et al. and the theories by Pan and Acrivos.     

UKF参数估计在航天器气动辅助变轨问题中的应用

为快速精确地求解气动辅助变轨问题,提出一种基于无损卡尔曼滤波(UKF)参数估计的数值求解方法。首先,针对气动辅助变轨问题,利用极大值原理将其转化为对应的两点边值问题;然后,以协态变量的初值作为估计参数,以末端条件为期望观测值,将该两点边值问题转化为参数估计问题,并应用UKF滤波算法求解。该算法基于估计理论,避免了计算传统数值方法所需要的梯度矩阵,同时克服了猜测协态变量初值的困难,降低了求解气动辅助变轨问题的难度。数值仿真表明,该算法结构简单,求解效率高,具有良好的鲁棒性。     

含三维接触问题的机翼下壁板翼肋对接孔结构断裂特性研究

飞机对接孔结构的损伤是飞机和许多工程结构中存在的一种典型损伤形式,它严重影响着结构的完整性和使用安全。因此,研究对接孔结构的断裂特性,具有重要的工程意义和实用价值。主要通过创建三维接触来考虑螺栓与螺栓孔间、垫片与下壁板内壁间的接触问题,应用有限元素法,建立合理的计算模型,计算翼肋对接孔结构在多种开裂模式下的应力强度因子,通过大量的计算分析,总结了机翼翼肋对接孔结构的断裂特性规律。计算结果和结论可作为该类结构损伤容限设计的参考依据。     

间接Legendre伪谱法的欠驱动航天器姿态运动轨迹跟踪

针对仅带有两组喷气推力器的非轴对称欠驱动刚性航天器,提出一种基于间接Legendre伪谱法的姿态运动轨迹跟踪控制算法。首先采用Legendre伪谱法(LPM)离线规划出系统的最短时间姿态机动参考轨迹。接着将实际运行轨迹与参考轨迹之间的偏差作为变量,根据Pontryagin极小值原理必要条件把系统姿态运动跟踪问题转化为一个两点边值问题(TPBVP)。最后采用 Legendre-Gauss-Lobatto(LGL)点将此两点边值问题离散转化为一个线性方程组来求解,避免了对传统Riccati微分方程的积分运算。数值仿真校验了本文基于间接Legendre伪谱法的姿态运动轨迹跟踪控制算法的有效性。     

Optimal station-keeping near Earth–Moon collinear libration points using continuous and impulsive maneuvers

In this study the gravitational perturbations of the Sun and other planets are modeled on the dynamics near the Earth–Moon Lagrange points and optimal continuous and discrete station-keeping maneuvers are found to maintain spacecraft about these points. The most critical perturbation effect near the L₁ and L₂ Lagrange points of the Earth–Moon is the ellipticity of the Moon’s orbit and the Sun’s gravity, respectively. These perturbations deviate the spacecraft from its nominal orbit and have been modeled through a restricted five-body problem (R5BP) formulation compatible with circular restricted three-body problem (CR3BP). The continuous control or impulsive maneuvers can compensate the deviation and keep the spacecraft on the closed orbit about the Lagrange point. The continuous control has been computed using linear quadratic regulator (LQR) and is compared with nonlinear programming (NP). The multiple shooting (MS) has been used for the computation of impulsive maneuvers to keep the trajectory closed and subsequently an optimized MS (OMS) method and multiple impulses optimization (MIO) method have been introduced, which minimize the summation of multiple impulses. In these two methods the spacecraft is allowed to deviate from the nominal orbit; however, the spacecraft trajectory should close itself. In this manner, some closed or nearly closed trajectories around the Earth–Moon Lagrange points are found that need almost zero station-keeping maneuver.