I am unsure about the virtual displacement and work definition even after looking through the definition and seeming to understand it. If we have(adsbygoogle = window.adsbygoogle || []).push({});

## \delta W = \displaystyle \sum_{i} \vec{F}_i \cdot \delta \vec{r}_i ##,

I can use,

## \delta \vec{r}_i = \sum_{i} \frac{\partial \vec{r}_i}{\partial q_k} \delta q_k ##,

and get to

## \delta W = \displaystyle \sum_{k}\sum_{i} \vec{F}_i \cdot \frac{\partial \vec{r}_i}{\partial q_k} \delta q_k ##.

So,

##\delta W = \sum_{k} \mathcal{F}_k \delta q_k ##.

Then in the derivation it says that this imples that

##\sum_{i} \vec{F}_i \cdot \frac{\partial \vec{r}_i}{\partial q_k}= \mathcal{F}_k = \frac{ \delta W}{\delta q_k} ##.

I thought that ##\delta W = \sum_{k} \frac{\partial W}{\partial q_k} \delta q_k ## and ## \mathcal{F}_k = \frac{\partial W}{\partial q_k} ##. This seems to imply that:

## \delta W = \sum_{i} \frac{\delta W}{\delta q_k} \delta q_k ##,

so where is the distinction, because I can't work out when to use thedeltas ords?

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# Virtual displacement and generalised forces

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