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General Work Functions

  1. Nov 25, 2014 #1
    I'm trying to derive a general work function (provided force and displacement vector-valued functions). Below are my best guesses. Can someone let me know whether these are valid?

    Rigid-System:
    ## \sum W = \int \left ( \sum \vec{F}(t)\cdot \vec{r}\,'(t) \right ) dt ##

    Deformable-system (n-forces):
    ## \sum W = \sum_{k=0}^{n} \left (\int ( \vec{F}_{k}(t)\cdot \vec{r}\,'(t)\,) dt \right) ##
     
  2. jcsd
  3. Nov 26, 2014 #2

    Simon Bridge

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    ##F(t)\cdot\vec r(t) = W(t)##

    So ##\sum W = \sum \vec F(t) \cdot \vec r(t)## notice: no integral on the RHS.

    Try starting from: ##\text{d}W = \vec F_{tot} \cdot \text{d}\vec r## and change variable to time.
     
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