constraint forces), is acceleration of the mass, and is the virtual displacement of the -th mass consistent with the constraints. The above equation holds true for all times so a definite integral with respect to must also be 0:

, the sum, and the integral can all be distributed:

Looking at the second term we can use the product rule to find the relation:

Variation and the time derivative commute (meaning ), so we can rearrange this to isolate our acceleration term:

Substituting

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