On Lambert’s problem and the elliptic time of flight equation: A simple semi-analytical inversion method

In the two-body model, time of flight between two positions can be expressed as a single-variable function and a variety of formulations exist. Lambert’s problem can be solved by inverting such a function. In this article, a method which inverts Lagrange’s flight time equation and supports the problematic 180°$180°$ transfer is proposed. This method relies on a Householder algorithm of variable order. However, unlike other iterative methods, it is semi-analytical in the sense that flight time functions are derived analytically to second order vs. first order finite differences. The author investigated the profile of Lagrange’s elliptic flight time equation and its derivatives with a special focus on their significance to the behaviour of the proposed method and the stated goal of guaranteed convergence. Possible numerical deficiencies were identified and dealt with. As a test, 28 scenarios of variable difficulty were designed to cover a wide variety of geometries. The context of this research being the orbit determination of artificial satellites and debris, the scenarios are representative of typical such objects in Low-Earth, Geostationary and Geostationary Transfer Orbits. An analysis of the computational impact of the quality of the initial guess vs. that of the order of the method was also done, providing clues for further research and optimisations (e.g. asteroids, long period comets, multi-revolution cases). The results indicate fast to very fast convergence in all test cases, they validate the numerical safeguards and also give a quantitative assessment of the importance of the initial guess.     

A robust semi-analytic method to solve the minimum ΔV two-impulse rendezvous problem

A novel semi-analytic approach is developed to determine the minimum $\mathrm{\Delta }V$ for a two-impulse rendezvous and validated both empirically and analytically. A previously published closed-form $\mathrm{\Delta }V$ estimate and the Lambert minimum energy transfer is used to establish upper and lower bounds of the minimum $\mathrm{\Delta }V$ transfer between two orbits. These bounds, in conjunction with the bisection method, operate on a nonlinear radical cost function to guarantee linear convergence. This approach has several real world applications including a low earth orbit (LEO) to highly elliptical orbit (HEO), and a HEO to retrograde geosynchronous orbit transfer. The minimum $\mathrm{\Delta }V$ estimates are better than those reported in the existing literature, while run times improved as much as two orders of magnitude over a fixed time Lambert solver. All singularity cases were addressed such that any orbital geometry, including Hohmann and radial elliptic transfers, converged to the global minimum $\mathrm{\Delta }V$. This approach will work for both coplanar and non-coplanar 3D geometries for any orbit type.     

人体手端点到点运动的优化轨迹生成与控制

考虑肢体肌肉的生理特征和肌肉收缩的动力学行为,利用肌肉等长收缩的最小功准则研究了人体手端点到点运动的优化轨迹生成与控制问题.讨论了肌肉收缩的动力学特性,建立水平面内上肢运动的动力学模型,提出将肌肉等长收缩的最小功准则作为优化的目标函数,运用最优化理论将手端点到点的运动问题转化为最优控制问题,设计了求解手端运动优化轨迹的迭代算法,得到了手端运动的控制规律和优化轨迹.算例仿真表明该方法对手端运动优化轨迹的预测是有效的.     

自适应捷变频雷达干扰方法分析及其效果度量

对自适应捷变频雷达的抗干扰性能进行分析,探讨了干扰自适应捷变频雷达的主要技术,如宽带阻塞干扰、回答式干扰、扫频式干扰等,并在功率准则基础上提出了一种更为全面、实用的干扰效果度量方法,为自适应捷变频雷达的干扰评估提供了一种新途径.     

一种新的RP-3航空煤油模拟替代燃料

为了遴选出符合RP-3航空煤油物理与化学特性的模拟替代燃料,综合分析了RP-3航空煤油的物理与化学特性。针对其物理与化学特性,确定了RP-3航空煤油模拟替代燃料的遴选指标（包括摩尔质量、氢碳比、十六烷值与低热值）。针对遴选指标,提出了由正癸烷、正十二烷、异十六烷、甲基环己烷及甲苯等五种组分组成的RP 3航空煤油模拟替代燃料,并对该模拟替代燃料中各组分的摩尔分数进行了优化。同时,对比分析了不同温度下该模拟替代燃料与RP 3航空煤油的密度与运动黏度。结果表明,当该模拟替代燃料中正癸烷、正十二烷、异十六烷、甲基环己烷及甲苯的摩尔分数分别为14%、10%、30%、36%与10%时,该模拟替代燃料的摩尔质量、氢碳比、十六烷值与低热值与RP 3航空煤油的相应数据非常吻合。同时,不同温度下该模拟替代燃料的密度与运动黏度变化趋势与RP-3航空煤油吻合较好。      

振动激发对激波反射的影响

定常激波反射分为规则反射和马赫反射,在不同条件下2种反射结构之间会相互转变。高超声速流动中的激波反射问题常面临高温气体效应,随着温度逐渐升高,最先出现的是空气分子振动激发。通过理论分析和定量计算,研究了振动激发对激波反射及其转变规律的影响。首先给出考虑振动激发的空气热力学模型,并分析其与量热完全气体的差异以及对激波关系的影响;接着分析在规则反射和马赫反射中,振动激发对激波反射流场的影响规律;最后讨论振动激发对激波反射转变2个准则点的影响。研究结果表明,振动激发使激波极线的整体轮廓变大,且这种差异在经过一次激波反射之后被明显放大,会对激波反射的流场产生重大影响;对于激波反射的转变,振动激发使转变的2个准则点都变大,且对规则反射向马赫反射转变的脱体准则影响更大。     

归一化参数蠕变模型的程序实现与验证

为了准确模拟实际构件的蠕变行为和应力松弛效应,在通用有限元程序环境下,利用其提供的用户可编程特性工具,将所发展的一种能完整描述蠕变3个阶段变形特征的归一化参数模型编制成用户子程序.考查了子程序计算结果与试验数据的差异、时间步长对计算结果的影响,并对不同规模有限元模型的计算耗时作了对比分析.针对变载(应力、温度)情形,在子程序中实现了时间硬化理论和应变硬化理论,并提出的介于两者之间的相对时间硬化理论.对带孔平板进行了实例计算,表明所发展的模型能够与有限元结果对实际结构进行蠕变模拟,计算结果的规律说明所发展的方法可较好地模拟实际构件的蠕变行为和应力松弛效应,验证了子程序的有效性.      

Niyama判据对铸件缩孔缩松预测的适用性

应用ProCAST有限元模拟软件包的Niyama判据对TiAl合金十字板状铸件中肉眼可见的宏观缩孔缩松进行了预测,并通过实验进行了验证.结果表明:对于Ti-47Al-2Cr-2Nb合金十字板状铸件,判据值主要受到铸件壁厚(冷速)的影响,判据值随铸件壁厚的增加而增大,宏观缩孔缩松最严重的区域不是判据值最小的区域,而判据值最小的区域只有显微缩松而没有宏观缩孔缩松,所以无法根据判据值大小来确定宏观缩孔和宏观缩松产生的位置及大小.分析表明,Niyama判据是一种基于枝晶间显微缩松的预测判据,其判据值适用于评定显微缩松产生的倾向性,可以较准确地预测出显微缩松产生的位置.由于宏观缩孔和宏观缩松形成机理与显微缩松不同,所以不宜用于壁厚悬殊的复杂铸件宏观缩孔缩松的预测.