一类非线性椭圆型方程非平凡解和分歧点的存在性

本文给出了所谓集中到列紧原理的另一形式，并利用它讨论了一类非线性椭圆型方程广义银和分歧点的顾在性。     

Periodic relative orbits of two spacecraft subject to differential gravity and electrostatic forcing

Coulomb forces between charged close-flying satellites can be used for formation control, and constant electric potentials enable static equilibria solutions. In this work, open-loop time-varying potential functions, which produce periodic, two-craft, Coulomb formation motions are demonstrated for the first time. This is done in the rotating Hill-Frame, with linearized gravity, and craft position components assumed in the form of simple harmonic oscillators. Substitution of the oscillatory functions into the dynamics, further constrains these functions, and yields necessary potential histories, to produce the periodic flow. The assumed position functions, however, are not arbitrary, since the dynamical model restricts what oscillatory trajectories are allowed. Specifically, a Hill-Frame integral of motion is derived, and this is used to show certain candidate periodic functions to be inadmissible. The system dynamics are then linearized to expose stability properties of the solutions, and it is established that asymptotic stability is impossible for all orbit families. Finally, the degree of instability in the assumed motions, over free parameter ranges, is determined numerically via the Floquet multipliers of the associated full-cycle state-transition matrices.     

关于跨声速流动问题的多重解

本文讨论了跨声速流小扰动方程Riemann问题的多重解及物理上可实现的解的判别。     

新能源接入配电网经济性与可靠性优化研究

为寻求新能源配电网的可靠性和经济性最优,实现新能源电源的优化配置,本文提出将可靠性和经济性同时作为两个优化目标,运用自适应粒子群优化法,对新能源电源进行多目标优化配置。以IEEE-RBTS Bus 6主馈线F4为例,通过系统仿真找到新能源配电系统可靠性与经济较均衡的Pareto最优解集,可根据决策者的偏好选择最优方案。本文的研究为新能源电力系统可靠性和经济评估提供了一个新的研究思路。     

小功率单轴燃气轮机及其功热并供装置变工况典型解析特性

采用动力机械变工况特性解析分析方法［１,２］,分析总结了使用离心式压气机的小功率单轴恒速燃气轮机稳态变工况的典型特性及一些定量规律。所得燃气轮机装置典型效率曲线及统计公式得到了实际数据的验证。计算了该种燃气轮机功热并供装置用饱和蒸汽供热时的典型情况及其他一些变工况性能,如大气温度的影响等     

非线性不平衡转子轴承系统周期解的预测

本文提出一种对非线性不平衡转子轴承系统周期解进行预测的新型算法,它利用系统周期解的稳态及瞬态信息,反解雅可比矩阵,实现对系统周期解的预测追踪,并利用反解得出的雅可比矩阵,求得系统周期解的Floquet乘子以判别其非线性稳定性。文中以刚性不平衡转子轴承系统为例,实现了周期解的预测追踪及非线性稳定性判别,说明了新算法的有效性。      

亚/超声速楔状流层流边界层速度与温度相似解及拟合解

利用相似变换获得了楔状流层流边界层无量纲流函数的3阶非线性常微分方程,用Runge-Kutta法求解微分方程获得了不同楔形角楔状流层流边界层无量纲速度随相似变量的变化曲线;推导了亚声速和超声速楔状流层流边界层无量纲温度关于相似变量的2阶线性齐次和非齐次微分方程,获得了温度分布的通解,恒壁温条件下亚声速楔状流和绝热壁面条件下超声速楔状流层流边界层无量纲温度解析解及指数函数形式的拟合解.以楔形角为0为例利用相似变换研究了超声速条件下气体压缩性及黏度随温度变化等因素对层流边界层速度与温度的影响,得出不可压缩常物性与可压缩变物性条件下无量纲速度相对误差绝对值小于9.8%的结论.研究表明:Pr越大贴近壁面处无量纲温度变化越剧烈;超声速条件下壁温低于绝热壁温时黏性耗散作用可以使层流边界层气体温度从壁面到主流间出现先升高后降低的变化.      

基于速度增量的空间绳系机器人中距离逼近过程最优轨迹规划

针对空间绳系机器人中距离逼近过程最优轨迹规划问题,提出了基于速度增量的多目标逼近轨迹优化方法,优化指标为总速度增量及逼近时间。首先建立逼近过程相对动力学模型及最优逼近轨迹优化模型,然后利用改进型非劣分类遗传算法得到相对逼近距离1.5 km内逼近轨迹的Pareto最优解。仿真结果表明,该方法可以揭示空间绳系机器人逼近距离1.5 km内逼近时间、燃料消耗、相对目标的面内视界角及速度增量次数之间的相互关系,能满足针对不同任务需求提供相应最优轨迹的要求。     

三阶幻方问题的代数解法

介绍了中国古代数学家甄鸾和杨辉关于三阶幻方的一个构造方法。用线性代数的方法构造三阶幻方约束方程组时,当自由未知量分别取1,2,3,…,9时,对应的方程组共有56组整数解,为了找出幻方的全部解,需要确定自由未知量取值的限制条件,由此对方程组中的自由未知量的取值进行了分类探讨,进而求出三阶幻方的全部解。利用线性代数的方法去探求三阶幻方的解法种数显然不是最简捷的,但却有完备的理论做保证。此外,提供了一个如何利用线性代数知识来解决实际问题的实例,并简介了三阶幻方所具有的奇妙的特性。     

Onboard orbit determination using GPS observations based on the unscented Kalman filter

Spaceborne GPS receivers are used for real-time navigation by most low Earth orbit (LEO) satellites. In general, the position and velocity accuracy of GPS navigation solutions without a dynamic filter are 25 m (1σ) and 0.5 m/s (1σ), respectively. However, GPS navigation solutions, which consist of position, velocity, and GPS receiver clock bias, have many abnormal excursions from the normal error range for space operation. These excursions lessen the accuracy of attitude control and onboard time synchronization. In this research, a new onboard orbit determination algorithm designed with the unscented Kalman filter (UKF) was developed to improve the performance. Because the UKF is able to obtain the posterior mean and covariance accurately by using the second-order Taylor series expansion through the sampled sigma points that are propagated by using the true nonlinear system, its performance can be better than that of the extended Kalman filter (EKF), which uses the linearized state transition matrix to predict the covariance. The dynamic models for orbit propagation applied perturbations due to the 40 × 40 geo-potential, the gravity of the Sun and Moon, solar radiation pressure, and atmospheric drag. The 7(8)th-order Runge–Kutta numerical integration was applied for orbit propagation. Two types of observations, navigation solutions and C/A code pseudorange, can be used at the user’s discretion. The performances of the onboard orbit determination were verified using real GPS data of the CHAMP and KOMPSAT-2 satellites. The results of the orbit determination were compared with the precision orbit ephemeris (POE) of the CHAMP and KOMPSAT-2 satellites.