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Virtual Work

最終更新：2008年10月29日 14:50

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Principle of Virtual Work

$\sum \mathbf{F}_i = 0 \Longleftrightarrow \delta W = 0$

$(\Longrightarrow)$ If $\sum \mathbf{F}_i = 0$ , then it must be true that for any virtual displacement $\delta\mathbf{r}$ , $\delta W = \sum \mathbf{F}_i \cdot \delta\mathbf{r} = 0$ .

$(\Longleftarrow)$ If $\delta W = 0$ holds for any virtual displacement $\delta\mathbf{r}$ , then it must be true that $\mathbf{F}_i = 0$ . Thus, $\sum \mathbf{F}_i = 0$ . (Otherwise, $\delta W = \sum \mathbf{F}_i \cdot \delta\mathbf{r} = 0$ wouldn't hold for *any* $\delta\mathbf{r}$ .)

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