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) --

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