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When do I need to use virtual work in writing the equations of motion?

  1. Jul 11, 2013 #1
    I'm studying for our comprehensive exam . I just need to clarify something. So the equation of motion for lagrangian dynamics is [itex]\frac{d}{dt}\frac{\partial L}{\partial\dot{q}_{i}}[/itex] = [itex]\frac{\partial L}{\partial {q}_{i}}[/itex]

    However, in my notes there are example which uses the principle of virtual work wherein [itex]\frac{d}{dt}\frac{\partial L}{\partial\dot{q}_{i}}[/itex] - [itex]\frac{\partial L}{\partial {q}_{i}}[/itex] = [itex]F_{q}[/itex]

    Then we look for [itex]F_{q}[/itex] using virtual work.

    However isn't [itex]\frac{d}{dt}\frac{\partial L}{\partial\dot{q}_{i}}[/itex] - [itex]\frac{\partial L}{\partial {q}_{i}}[/itex] = 0 ????
     
  2. jcsd
  3. Jul 11, 2013 #2
    I think I can help you, but I don't want to answer without knowing what F sub q stands for just in case I make things worse. Can you specify what it represents please?
     
  4. Jul 11, 2013 #3
    q is the generalized coordinate.

    For example if I have r (radial distance) as generalized coordinate I'll have


    [itex]\frac{d}{dt}\frac{\partial L}{\partial\dot{r}}[/itex] - [itex]\frac{\partial L}{\partial {r}}[/itex] = [itex]F_{r}[/itex]
     
  5. Jul 11, 2013 #4

    WannabeNewton

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