Broad-search algorithms for the spacecraft trajectory design of Callisto–Ganymede–Io triple flyby sequences from 2024 to 2040, Part II: Lambert pathfinding and trajectory solutions

Triple-satellite-aided capture employs gravity-assist flybys of three of the Galilean moons of Jupiter in order to decrease the amount of ΔV required to capture a spacecraft into Jupiter orbit. Similarly, triple flybys can be used within a Jupiter satellite tour to rapidly modify the orbital parameters of a Jovicentric orbit, or to increase the number of science flybys. In order to provide a nearly comprehensive search of the solution space of Callisto&ndash;Ganymede&ndash;Io triple flybys from 2024 to 2040, a third-order, Chebyshev's method variant of the p-iteration solution to Lambert's problem is paired with a second-order, Newton&ndash;Raphson method, time of flight iteration solution to the <sub>Vsub><sub>∞sub>-matching problem. The iterative solutions of these problems provide the orbital parameters of the Callisto&ndash;Ganymede transfer, the Ganymede flyby, and the Ganymede&ndash;Io transfer, but the characteristics of the Callisto and Io flybys are unconstrained, so they are permitted to vary in order to produce an even larger number of trajectory solutions. The vast amount of solution data is searched to find the best triple-satellite-aided capture window between 2024 and 2040.     

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&rsquo;s problem can be solved by inverting such a function. In this article, a method which inverts Lagrange&rsquo;s flight time equation and supports the problematic 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&rsquo;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 for a two-impulse rendezvous and validated both empirically and analytically. A previously published closed-form estimate and the Lambert minimum energy transfer is used to establish upper and lower bounds of the minimum 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 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 . This approach will work for both coplanar and non-coplanar 3D geometries for any orbit type.     

A statistical study of hot flow anomalies using Cluster data

Hot flow anomalies (HFAs) are studied using observations of the RAPID suprathermal charged particle detector, the FGM magnetometer, and the CIS plasma detector aboard the four Cluster spacecraft. Previously, we studied several specific features of tangential discontinuities on the basis of Cluster measurements in February&ndash;April 2003. In this paper, we confirm the following results: the angle between the Sun direction and the tangentional discontinuity (TD) normal is larger than 45° during HFAs, the magnetic field directional change is large. We then present evidence for a new necessary condition for the formation of HFAs, that is, the solar wind speed is significantly (about  ss="imgLazyJSB inlineImage" height="18" width="166" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0273117708000720-si7.gif">script>style="vertical-align:bottom" width="166" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0273117708000720-si7.gif">script>) higher than the long-term average. The existence of this condition is also confirmed by simultaneous ACE MAG and SWEPAM solar wind observations at the L1 point 1.4 million km upstream of the Earth. The results are compared with recent hybrid simulations.     

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.&nbsp;     

恒定磁场对α—淀粉酶的生物效应初探

利用荧光光谱探讨了磁场引起α—淀粉酶构象的变化及其原因。α—淀粉酶在２０℃、ｐＨ６．６的磷酸盐缓冲溶液中，经０．０５～０．２５Ｔ静磁场作用不同时间均能引起荧光强度的明显变化，其变化程度与磁场强度和磁化时间有关，但不伴有最大发射峰位移。用分光光度法考察了磁场对溶解α—淀粉酶活性的影响，未发现活性的明显变化，其结果与磁场对固定化α—淀粉酶活性的影响不一致。提出了磁场对酶分子的生物效应与酶存在形式有关     

Hoff型夹层板振动分析的边界积分方程法

&nbsp;本文利用静力问题的基本解建立了Hoff型夹层板振动分析的边界积分方程。在数值实现过程中,边界上和区域内的未知函数均釆用线性插值以提高计算精度。数值结果表明本文方法具有未知量少和计算精度高等优点。对于低阶频率,本文结果与精确解的误差不大于1％。     

通用模糊控制器研究

讨论了通用模拟控制器的设计,用单片机构成硬件电路,用软件实现模糊控制算法,来实现对被控对象的模糊控制。这种模糊控制的特点是资源开销小,灵活性高,通用性强,可广泛应用于家用电器的自动控制系统中。     

飞机翼面结构布局综合设计方法研究

为了探讨飞机翼面结构主要纵横骨架的最佳布局问题,并提供符合工程实际的、用于概念设计阶段的飞机结构设计方法,本文采用分级优化与集成的策略,该策略分为3个层次。第一个层次为拓扑优化,并由此确定纵向骨架的个数与位置的最优布局;第二个层次为尺寸优化,它用来确定翼面的中间参数;第三个层次为稳定性准则优化,它确定横向骨架的个数与位置的最优布局。在分级优化的3个层次中,拓扑优化是独立的,尺寸优化与稳定性准则优化是相互耦合的。以国外某飞机机翼为例,结果表明本文提出分级优化的思路与所采用的集成方法是可行的,并且具有很好的数值效果。作者认为：它对从事飞机结构设计的人员有一定的指导性和参考价值,值得在飞机设计部门推广应用。最后,总结给出5点结论供参考。