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

[jhosamelly]

I'm studying for our comprehensive exam . I just need to clarify something. So the equation of motion for lagrangian dynamics is $\frac{d}{dt}\frac{\partial L}{\partial\dot{q}_{i}}$ = $\frac{\partial L}{\partial {q}_{i}}$

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

Then we look for $F_{q}$ using virtual work.

However isn't $\frac{d}{dt}\frac{\partial L}{\partial\dot{q}_{i}}$ - $\frac{\partial L}{\partial {q}_{i}}$ = 0 ?

 

[Joey21]

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?

 

[jhosamelly]

q is the generalized coordinate.

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


$\frac{d}{dt}\frac{\partial L}{\partial\dot{r}}$ - $\frac{\partial L}{\partial {r}}$ = $F_{r}$

 

[WannabeNewton]

The second equation is for when non-conservative forces are present; one can then use the virtual work principle to find the $F_{q}$ (the non-conservative generalized forces) and incorporate them into the modified Euler-Lagrange equations written above. See here: http://ocw.mit.edu/courses/mechanic...control-i-spring-2007/lecture-notes/lec14.pdf