Sure: what I was referring to in the example that I gave was the q-dot that appears in the denominator of the expression of the partial derivative of the Lagrangian.
Ah. I think I get it now. I misinterpreted what you meant by the word "see" (in "My advice is to see the dot..."). I thought you meant, "understand that in fact q-dot is an independent variable" when in fact you meant (AFAICT) "pretend that q-dot is an independent variable even though in fact it is not."
