作者chopriabin (Be a Dissertation-maker)
看板NTUMystery
标题[心得] 冰冷密室与博士们的前言(原文与翻译)
时间Wed Mar 23 16:05:39 2005
The uniqueness theorems of Kirchhoff and Neumann are the foundation for the
method of potentials. For, when uniqueness of solution is established, one
needs to find only a solution of a given boundary-value problem: that
solution is the solution.
But it is essential for our theory to be able to violate the uniqueness of
solution in one way or another. We know that elastic columns can buckle,
thin shells may collapse, airplane wings can flutter, machinery can become
unstable in one sense or other. The word"stability" has many meanings; to
define a stability problem we must define the sense of the word stability.
But a largr class of practical stability problems is connected with the loss
of uniqueness of solution. Under certain circumstances two or more solutions
may become possible; some of these may be dangerous from engineering point
view or undesirable for the function of the machinery; and the circumstances
are said to cause inatability.
克希赫夫和诺伊曼的唯一性定理是位能法的基础。因为,一但有了解的唯一性,我们只需
找出所给定边界值问题的解;那麽那个解就是唯一解。
然而,重要的是,我们的理论也许在其他状况下会违反解的唯一性。我们知道在某种意义
下,弹性柱体会弯曲,薄壳可能会崩坏,飞机机翼会震动,机械会变得不稳定。稳定性一
辞有许多意义;要定义稳定性问题我们必须先定义稳定性一辞的意义。但是一大部分实际
的稳定性问题与解的唯一性的缺乏有关。在某些情况下可能会有两解或三解。从工程的观
点来看,这些状况可能是危险的或不被机械功能所期许发生的;一切的这些情况皆可说是
引发了不稳定性。
--
Not knowing when the Dawn will come
I open every Door
Or Has it feathers, like a Bird
Or Billows, like a Shore.
Emily Dickinson(1830-1886)
--
※ 发信站: 批踢踢实业坊(ptt.cc)
◆ From: 140.112.50.208
1F:推 Pets:太感谢了~~^__^ 61.63.7.60 03/23
2F:推 searoad:翻出来还是看不懂吧-___-? 203.73.50.109 03/23
3F:推 chopriabin:也许翻译与原文还有错,有修正版我会再放上去. 140.112.50.204 03/24
4F:推 chopriabin:这段前言很多可以用高中物理的概念来理解喔! 140.112.50.204 03/25
5F:→ chopriabin:完全不需要藉由任何数学方程式. 140.112.50.204 03/25
6F:→ chopriabin:有兴趣的人可以与我讨论.因为po版的话好像会술 140.112.50.204 03/25
7F:→ chopriabin:离题了些... 140.112.50.204 03/25
8F:推 MikaHakkinen:高中物理我也不懂 Orz 220.139.147.62 03/25