论文标题
关于兰伯特问题的一些简单结果
Some simple results about the Lambert problem
论文作者
论文摘要
我们简单地证明了有关兰伯特问题的一些简单陈述。我们首先重述并谴责开普勒弧的已知存在和独特性结果。在某些情况下，我们还证明经过的时间是自然参数的凸功能。我们的陈述和证明并不能区分开普勒圆锥部分的三种类型，即椭圆形，抛物线和双曲线。我们还证明了非唯一性结果和非跨性别结果。我们没有开发任何解决方案算法，将自己限制在如此有用的先验问题上：我们应该期望多少个解决方案？我们可以确定牛顿方法会融合吗？
We give simple proofs of some simple statements concerning the Lambert problem. We first restate and reprove the known existence and uniqueness results for the Keplerian arc. We also prove in some cases that the elapsed time is a convex function of natural parameters. Our statements and proofs do not distinguish between the three types of Keplerian conic section, elliptic, parabolic and hyperbolic. We also prove non-uniqueness results and non-convexity results. We do not develop any algorithm of resolution, limiting ourselves to such obviously useful a priori questions: How many solutions should we expect? Can we be sure that the Newton method will converge?
