开普勒方程与角动量：历史视角、批判性分析及其对轨道力学/动力学、数学与物理学发展的启示
物理学史与哲学
2021-09-03 v3 物理教育
摘要
在开普勒方程于《新天文学》中表述并发表至今四个多世纪后，该方程依据其第二（“面积”）定律将行星轨道的偏近点角（以及中间的真近点角）与均匀流逝的时间相联系；而在轨道力学发展过程中，后来与第二定律相关并形式化推导出的不存在的（零值）横向加速度受到了质疑。本文也简要提示了其对椭圆积分、辛积分、辛几何/拓扑的一些启示，以及在具有增强的中心力与转矩力的多层次、标度不变力学/动力学语境下物理连续统与数学连续统之间的联系。
引用
@article{arxiv.2012.00749,
title = {Keplers's Equation and Angular Momentum: Historical Perspective, Critical Analysis and Implications for Development of the Orbital Mechanics/Dynamics, Mathematics and Physics},
author = {Slobodan Nedic},
journal= {arXiv preprint arXiv:2012.00749},
year = {2021}
}
备注
The submission has been revised due to erroneously - wrong sign in the second part in the angle-bracket of equation 2 - derived expression for the transverse acceleration. While the basic conclusions regarding the untenability of the Prime integral of angular momentum and the corresponding Cyclic Coordinate have remained unchanged, this leads to investigation of the invariance in mechanics