RECENT ADVANCES IN DYNAMICS.
RECENT ADVANCES IN DYNAMICS.
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动力学的最新进展。
DOI：
10.1126/science.51.1307.51
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发表时间：
1920
期刊：
影响因子：
56.9
通讯作者：
G. Birkhoff
中科院分区：
文献类型：
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作者：
G. Birkhoff
为了了解自该日以来采取的新方向，有必要回顾一下以前的主要事态发展。在这样做的时候，我们将自始至终自由地提到三个机构的问题以示说明。在牛顿时代之前，动力系统的概念还不存在。利用他的万有引力定律，牛顿能够把地球、太阳和月亮本质上看作是三个相互作用的粒子：L作用的粒子兰德。借助于他的流动微积分，他能够用微分方程式来表述它们的运动定律。这里的自变量是时间，因变量是三体的九个坐标。这样一组常微分方程组构成了动力系统的典型体现，构造起来没有特别的困难。牛顿和他的继任者的目标是为各种动力系统找到关于时间的坐标的显式表达式，就像牛顿在两个物体的问题中所做的那样。尽管取得了显著的成就，但三体问题和其他类似问题的微分方程式仍然无视“积分”。尽管没有明确的坐标表达式，牛顿还是能够从几何的角度来看待月球理论。欧拉、拉普拉斯和其他人发明了基于系列的更精确的分析方法。在这两种情况下，扰乱运动的物体
To understand the new direction taken since that date it is necessary to recall the main previous developments. In doing this, and throughout, we shall refer freely for illustration to the problem of three bodies. The concept of a dynamical system did not exist prior to Newton's time. By use of his law of gravitation Newton was able to deal with the Earth, Sun, and Moon as essentially three mutually'att: l~ acting particles, rand, by the. aid of his fluxional calculus he was in a posi-, tion to formulate their law of motion by means of differential equations. Here the independent variable is the time and the dependent variables are the nine coordinates of the three bodies. Such a set of ordinary differential, equations form the characteristic masthemat-, ical embodiment of a dynamical system, and, can be constructed without especial difficulty. The aim of Newton and his successors was~ o find explicit expressions for the coordinates in terms of the time for various dynamical systems, just as Newton was able to do in the problem of two bodies. Despite notable successes, the differential equations of the problem of three bodies and of other analogous problems continued to defy" integration." Notwithstanding the lack of explicit expressions for the coordinates, Newton was able to treat the lunar theory from a geometrical point of view. Euler, Laplace, and others invented more precise analytical methods based upon series. In both cases the bodies which are disturbing the motion of the