Kepler-Coulomb问题的速度空间牛顿解法
Newtonian approach for the Kepler-Coulomb problem from the point of view of velocity space
摘要：
的开普勒-库仑问题的速端图，即其速度矢量跟踪的路径，被证明是一个圆，然后它被用来调查其他属性的运动。我们得到的配置空间轨道的问题从初始条件开始，只使用合成几何的方法，所以接近牛顿的方法。该方法适用于椭圆，抛物和双曲轨道，它甚至可以用来推导卢瑟福的关系，从散射截面可以很容易地评估。我们认为我们的讨论既有趣又有用，因为它以纯粹几何的方式将初始条件与相应的轨迹联系起来，在这个过程中揭示了一些很少讨论的有趣联系。
英文摘要：
The hodograph of the Kepler-Coulomb problem, that is, the path traced by its velocity vector, is shown to be a circle and then it is used to investigate other properties of the motion. We obtain the configuration space orbits of the problem starting from initial conditions given using nothing more than the methods of synthetic geometry so close to Newton's approach. The method works with elliptic, parabolic and hyperbolic orbits; it can even be used to derive Rutherford's relation from which the scattering cross section can be easily evaluated. We think our discussion is both interesting and useful inasmuch as it serves to relate the initial conditions with the corresponding trajectories in a purely geometrical way uncovering in the process some seldom discussed interesting connections.
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。
