ME 5550 Intermediate Dynamics
Principle of Virtual Work
Principle of Virtual Work
If a mechanical system whose configuration is defined by a set of independent generalized
coordinates qk (k  1,..., n) is in static equilibrium, then the generalized force associated
with each of the qk (k  1,..., n) must be zero. That is,
Fqk  0
(k  1, , n)
Recall that if a system has "n" degrees of freedom, then "n" independent generalized
coordinates are required to completely define its configuration. Hence, for an "n" degree of
freedom system in static equilibrium, we can write "n" independent equilibrium equations.
Example
For the simple pendulum shown, we can calculate the
torque M required to hold the bar at some angle  by using
the principle of virtual work as follows:
F   F W   F M  0


 R vG 
 RB 
 W 
  M 

 
 




L


  mg j  cos( ) i  sin ( ) j     Mk    k 
2


or
L
M  mg sin ( )
2
Note: The contribution of the weight force could also have been calculated using the
potential energy function for weight. That is,
 F W  
 
L
L


mg
cos(

)


mg
sin( ) .


 
2
2

Kamman – ME 5550 – page: 1/1