从圆形轨道到椭圆轨道：开普勒运动的几何方法
From circular paths to elliptic orbits: A geometric approach to Kepler's motion
摘要：
速端图（hodograph），即物体在速度空间中的轨迹，由汉密尔顿于1846年引入，作为研究某些动力学问题的替代方法。开普勒问题的速端图随后被研究并被证明是一个圆，它接下来被用来研究运动的其他一些性质。本文从给定的初始条件出发，试图用综合几何的方法，用一种牛顿的方法，给出一种追踪开普勒问题中速端图和相应位形空间轨道的新方法。我们所有的几何构造只需要直尺和圆规。
英文摘要：
The hodograph, i.e. the path traced by a body in velocity space, was introduced by Hamilton in 1846 as an alternative for studying certain dynamical problems. The hodograph of the Kepler problem was then investigated and shown to be a circle, it was next used to investigate some other properties of the motion. We here propose a new method for tracing the hodograph and the corresponding configuration space orbit in Kepler's problem starting from the initial conditions given and trying to use no more than the methods of synthetic geometry in a sort of Newtonian approach. All of our geometric constructions require straight edge and compass only.
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。
