Generalized force
From Wikipedia, the free encyclopedia
It has been suggested that this article or section be merged with Generalized forces . (Discuss) |
The idea of a Generalized Force is a concept stemming from Lagrangian mechanics. It is a consequence of the application of generalized coordinates to a system undergoing acceleration.
When a particle undergoes a virtual displacement under the influence of a force the virtual work done by that force is given by:
Translating to generalized coordinates:
and by reversing the order of summation we get
It is from this formulation that the idea of a generalized force stems. The above equation can be written as
where
is called the generalized force associated with the coordinate qj.
Since Qjqj has the dimension of work, Qj will have the dimension of force if qj is a distance, and the dimension of torque if qj is an angle.