Generalized Forces: Understanding i & j - Physics Help

[sayf alawneh]

hello guys
i like physics specially the classical dynamics but am finding it hard to understand those letters (i , j ) now am studying about the generalized forces corresponded with generalized coordinates
and there is an equation in the attached pic with this thread
can anybody help me and explain for me in words what this equation mean (for i's and j's)??
if "k" introduces the # of constraints
and "n" introduces the # of degrees of freedom or generalized coordinates
and j=(1,2,...k)
and i=(1,2,...n)

 

[FactChecker]

I don't think that k is the number of constraints. It is the dimension of the coordinate space that the force F is known in. F_j is the component of F in the direction of the dimension x_j. The component of Q in direction of dimension i is the summation of the F_j components of F in direction i. In other words, the component of force Q in direction i can be found from F's original components in its original coordinates x_j.