兰伯特方程的一种快速解法

An Efficient Procedure for the Solution of Lambert Problem

首先简要阐述了兰伯特方程的拉格朗日形式,进而根据超几何函数的连分数表达形式推导出无量纲转移时间对参数x的一、二阶导数。在此基础上,采用Halley迭代公式给出求解兰伯特方程的具体步骤。

This paper describes a procedure that provides an efficient solution for Lambert's problem.Based on the Gooding and Battin approach,the second derivative of the flight time on the form of hypergeometric function is derived.Three iterations of the process shall always suffice to yield an accurate value when using Halley's cubic iteration process to evaluate the unknown parameter x with a proper initial value.