不用解微分方程的开普勒定律的简单推导
A simple derivation of Kepler's laws without solving differential equations
摘要：
像牛顿一样，用离散时间的方法来处理运动，用速度和加速度的几何表示，我们不用解微分方程就能得到开普勒定律。牛顿工作中的困难部分，当它要求椭圆的非平凡性质时，通过引入极坐标来避免。然后，简单地重新考虑牛顿的图形，自然会导出速度的显式表达式和轨迹方程。这个推导，可以完全理解的初学者在大学（甚至之前），可以被认为是第一次应用力学概念的物理问题的伟大历史和教学的兴趣。
英文摘要：
Proceeding like Newton with a discrete time approach of motion and a geometrical representation of velocity and acceleration, we obtain Kepler's laws without solving differential equations. The difficult part of Newton's work, when it calls for non trivial properties of ellipses, is avoided by the introduction of polar coordinates. Then a simple reconsideration of Newton's figure naturally leads to en explicit expression of the velocity and to the equation of the trajectory. This derivation, which can be fully apprehended by beginners at university (or even before) can be considered as a first application of mechanical concepts to a physical problem of great historical and pedagogical interest.
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。
