Singularities in Classical Mechanical Systems
Singularities in Classical Mechanical Systems
复制标题
经典机械系统中的奇点
DOI：
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发表时间：
1981
期刊：
影响因子：
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通讯作者：
R. Devaney
中科院分区：
文献类型：
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作者：
R. Devaney
经典力学系统的运动方程中的奇异性通常在系统的全局相图中起主导作用。奇点是指系统不确定的一个点或一组点，如在n体问题中两个或多个粒子碰撞的情况。这种奇异性往往导致复杂的全局轨道结构。不仅某些解趋向于脱离相空间，而且附近的解也趋向于以不稳定或不可预测的方式表现。由于这种不稳定的行为，对这种系统的数值研究往往是不确定的。而幂级数或其他分析方法往往只能给出奇点附近解的非常局部的描述，无法给出系统整体复杂性的暗示。
Singularities in the equations of motion of a classical mechanical system usually play a dominant role in the global phase portrait of the system. By a singularity we mean a point or set of points where the system is undefined, as in the case of a collision between two or more of the particles in the n-body problem. Such singularities often lead to a complicated global orbit structure. Not only do certain solutions tend to run off the phase space, but also nearby solutions tend to behave in an erratic or unpredictable manner. Numerical studies of such systems are often inconclusive because of this erratic behavior. And power series or other analytic techniques often yield only a very local description of solutions near the singularity, one which gives no hint of the global complexity of the system.