So I'm doing some work from Taylor's mechanics book. He says for the problems in the book, we require the system to be holonomic - that is the number of generalized coordinates = number of Deg. of freedom. Why does this have to be the case?
I have been looking through his proof for a single particle, where he proves the Lagrangian, for the correct path taken by the particle, minimizes the action integral, but he doesn't say 'for this step in the proof to be true, we require the system to be holonomic'.
So why does this feature have to be true?