virtual displacement from the equilibrium position is given by
:where denote the virtual displacements of each point in the body.

Now assume that each depends on the generalized coordinates then
:and
:

The terms
:are the generalized forces acting on the system. Kane shows that these generalized forces can also be formulated in terms of the ratio of time derivatives,
:where is the velocity of the point of application of the force .

In order for the virtual work to be zero for an arbitrary

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