发表机构
Naval Postgraduate School（海军研究生院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文修正了三体问题Nechvile坐标系下航天器运动方程中外力项的形式，结合质量流量率方程修正火箭方程，经Birkhoff理论求解地月任务表明可节省80%推进剂。
AI 中文摘要
自20世纪60年代以来，限制性三体问题中Nechvile坐标系下的无控运动方程已广为人知。人们似乎认为在这些方程中加入外力相当简单：只需在加速度方程中添加单位质量外力项即可。但本文证明该说法不成立，实际上，添加的通用外力必须乘以(1 + e cosθ)的-3次方，其中e为主天体的相对偏心率，θ为位于 barycenter（ barycenter：质心）的旋转坐标系的真近点角。此外，将该结果与质量流量率方程结合时，由于运动方程中二次项与三次项不匹配，会产生若干令人惊讶的结果，这进而导致火箭方程本身需做相应修正。对一个示例地月空间任务问题的Birkhoff理论求解表明，采用正确的代价泛函可实现80%的推进剂节省，而常用的二次代价函数所消耗的推进剂是最小值的2倍以上。
英文摘要
The uncontrolled equations of motion in the Nechvile frame for the restricted three-body problem have been well-known since at least the 1960s. It would seem that adding an external force to these equations is quite trivial: simply add an external force per mass term to the acceleration equations. Here we show that the last statement is not true. In fact, we show that the additive generic external force must be multiplied by the inverse of $(1 + e \cosθ)^3$ where $e$ is the relative eccentricity of the primaries and $θ$ is the true anomaly of the rotating frame located at the barycenter. Furthermore, when this result is combined with the mass flow rate equation, it generates several surprising results due to the mismatch between the resulting quadratic term and the cubic term in the equations of motion. This leads to a corresponding modification of the rocket equation itself. A Birkhoff-theoretic solution to an illustrative cislunar space mission problem shows propellent savings of 80% with the use of the correct cost functional. The popular quadratic cost utilizes more than $2X$ the minimum propellant consumption.
Journal refDixon, M. J. and Ross, I. M., "Nuances in Propellant Computation in the Elliptic Restricted Three- Body Problem," Journal of Guidance, Control and Dynamics, Vol. 49, No. 1, Jan. 2026
