Lambert's problem的评论
Review of Lambert's problem
摘要：
Lambert问题是两点和时间约束的轨道边值问题。它是天体力学和天体动力学中研究最广泛的问题之一，因此，它一直吸引着数学家和工程师的兴趣。它的解决方案在于算法的基础，例如，轨道确定、轨道设计（飞行任务规划）、空间会合和拦截、空间碎片相关、导弹和航天器目标确定。有大量的文献讨论了多年来开发的解决兰伯特问题的各种方法。我们已经收集了70多篇论文，当然，这个问题在大多数天体动力学和天体力学教科书中都有涉及。从我们对文件的分析中，我们已经能够确定六个或七个主要的解决方法，每个方法都与一些修订和变化有关，以及许多，可以说，很少或根本没有后续发展的次要研究路线。我们已经确定了大量的文献与建议的解决方案，在许多情况下，通过与其他方法的性能比较补充。我们已经审查和组织现有的参考文献对兰伯特的问题，我们已经进行了定量比较现有的方法，其解决方案。分析是基于以下问题：自由参数的选择，迭代次数，一般性的数学公式，适用性的限制（退化，域的参数，特殊情况和特点），准确性，并适合自动执行。最后，我们测试了每个代码的性能。结合最佳品质的求解器是Bate的算法通过通用变量与Newton-Raphson和Izzo的Householder算法。前者是最快的，后者表现出最好的速度，鲁棒性和准确性之间的比例。
英文摘要：
Lambert's problem is the orbital boundary-value problem constrained by two points and elapsed time. It is one of the most extensively studied problems in celestial mechanics and astrodynamics, and, as such, it has always attracted the interest of mathematicians and engineers. Its solution lies at the base of algorithms for, e.g., orbit determination, orbit design (mission planning), space rendezvous and interception, space debris correlation, missile and spacecraft targeting. There is abundancy of literature discussing various approaches developed over the years to solve Lambert's problem. We have collected more than 70 papers and, of course, the issue is treated in most astrodynamics and celestial mechanics textbooks. From our analysis of the documents, we have been able to identify six or seven main solution methods, each associated to a number of revisions and variations, and many, so to say, secondary research lines with little or no posterior development. We have ascertained plenty of literature with proposed solutions, in many cases supplemented by performance comparisons with other methods. We have reviewed and organized the existing bibliography on Lambert's problem and we have performed a quantitative comparison among the existing methods for its solution. The analysis is based on the following issues: choice of the free parameter, number of iterations, generality of the mathematical formulation, limits of applicability (degeneracies, domain of the parameter, special cases and peculiarities), accuracy, and suitability to automatic execution. Eventually we have tested the performance of each code. The solvers that incorporate the best qualities are Bate's algorithm via universal variables with Newton-Raphson and Izzo's Householder algorithm. The former is the fastest, the latter exhibits the best ratio between speed, robustness and accuracy.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
