N-body dynamics on closed surfaces: the axioms of mechanics.
N-body dynamics on closed surfaces: the axioms of mechanics.
复制标题
闭合表面上的 N 体动力学：力学公理。
DOI：
10.1098/rspa.2016.0020
复制
发表时间：
2016
期刊：
影响因子：
--
通讯作者：
Boatto S
中科院分区：
文献类型：
--
作者：
Boatto S
我们理解粒子动力学数学基础的一个主要挑战是黎曼曲面上 N 体和 N 涡动力学的公式。在本文中，我们展示了在考虑表面固有几何形状所发挥的作用时，这两个问题实际上是如何密切相关的。这使得能够使用最近导出的具有度量的一般封闭可微表面上的点涡流结果来直接推导点质量的动力学。我们发现，一般来说，开普勒定律并不成立。更重要的是，即使牛顿第一定律（惯性定律）在曲率可变的封闭曲面（例如椭球体）上也失效。
A major challenge for our understanding of the mathematical basis of particle dynamics is the formulation of N-body and N-vortex dynamics on Riemann surfaces. In this paper, we show how the two problems are, in fact, closely related when considering the role played by the intrinsic geometry of the surface. This enables a straightforward deduction of the dynamics of point masses, using recently derived results for point vortices on general closed differentiable surfacesMendowed with a metricg. We find, generally, that Kepler's Laws do not hold. What is more, even Newton's First Law (the law of inertia) fails on closed surfaces with variable curvature (e.g. the ellipsoid).