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. 克希赫夫和諾伊曼的唯一性定理是位能法的基礎。因為，一但有了解的唯一性，我們只需 找出所給定邊界值問題的解；那麼那個解就是唯一解。 然而，重要的是，我們的理論也許在其他狀況下會違反解的唯一性。我們知道在某種意義 下，彈性柱體會彎曲，薄殼可能會崩壞，飛機機翼會震動，機械會變得不穩定。穩定性一 辭有許多意義；要定義穩定性問題我們必須先定義穩定性一辭的意義。但是一大部分實際 的穩定性問題與解的唯一性的缺乏有關。在某些情況下可能會有兩解或三解。從工程的觀 點來看，這些狀況可能是危險的或不被機械功能所期許發生的；一切的這些情況皆可說是 引發了不穩定性。 -- 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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