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First of all,the notation you've given is wrong.DocAl said:I'm missing your point, Daniel. If I define work in the usual way,[itex] dW=\vec{F}\cdot d\vec{r}[/itex],why can't I consider work to be a function of time? Certainly its rate of change with time is not (necessarily) zero!

[tex] \delta W=:\vec{F}\cdot d\vec{r} [/tex]

,simply because it's not a differential,but a one-form.

You cannot define "work" by the (wrongly written) formula,you define "differential work" which is not the same thing,obviously.

Even if i repeat myself,this is the definition of work:

[tex] W_{1\rightarrow 2} [\vec{r}] =:\int_{1}^{2} \vec{F}(\vec{r}(t),\dot{\vec{r}}(t),t)\cdot \vec{n} dl [/tex]

It is a functional of [itex] \vec{r}(t) [/itex].

My question is,to you and to Marlon:

What is the mathematical significance of these "animals"?

[tex] \frac{dW_{1\rightarrow 2}[\vec{r}]}{dt} [/tex]

and the most interesting by far:

[tex] \frac{\delta W}{dt}[/tex] ??

Daniel.

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