# A Generalized force

1. Oct 28, 2016

### 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 any body 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)

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2. Oct 28, 2016

### 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. Fj is the component of F in the direction of the dimension xj. The component of Q in direction of dimension i is the summation of the Fj 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 xj.