论文标题
牛顿的离散动态
Newton's discrete dynamics
论文作者
论文摘要
1687年，艾萨克·牛顿（Isaac Newton）发表了哲学\ Naturalis Principia Mathematica，其中制定了经典的分析动态。但是牛顿还制定了一个离散的动力学，即中心差算法，称为Verlet算法。实际上，牛顿利用核心区别得出了他的第二定律。中心差算法用于计算机模拟中，其中几乎所有分子动力学模拟都是使用Verlet算法或中心差算法的其他重新进行的。在这里，我们表明，纽顿算法为开普勒方程获得的离散动力学具有与分析动力学相同的解决方案。天体的离散位置位于椭圆形上，这是用于分析溶液的哈密顿量附近的影子哈密顿量的确切解决方案。
In 1687 Isaac Newton published PHILOSOPHIÆ\ NATURALIS PRINCIPIA MATHEMATICA, where the classical analytic dynamics was formulated. But Newton also formulated a discrete dynamics, which is the central difference algorithm, known as the Verlet algorithm. In fact Newton used the central difference to derive his second law. The central difference algorithm is used in computer simulations,where almost all Molecular Dynamics simulations are performed with the Verlet algorithm or other reformulations of the central difference algorithm. Here we show, that the discrete dynamics obtained by Newtons algorithm for Kepler's equation has the same solutions as the analytic dynamics. The discrete positions of a celestial body are located on an ellipse, which is the exact solution for a shadow Hamiltonian nearby the Hamiltonian for the analytic solution.
