There might have been multiple questions like the one to follow, but I have not been able to find a satisfactory answer (or just hasn’t been able to understand the answers), so I guess I shall ask it anyway. When introducing d’Alembert’s principle, Goldstein in his text on classical mechanics says that sliding friction is a force of constraint and that such situations are out of discussion. I have two questions about this statement.
- Why is sliding friction a force of constraint?
If, for example, we have a coin rolling in a weird way, say, down an inclined plane, then I see that there are nontrivial relations between coordinates needed to describe the motion of the coin completely. These relations arise from rolling, which is due to friction, so it’s a force of constraint in this case. But if we have a block that is being pulled weirdly around the plane, I don’t see the kind of relationship friction would establish between the coordinates necessary do describe its motion (x-y coordinates to describe the position of the block and some $\phi$ to describe its orientation)
- Even if we accept that sliding friction is a force of constraint, why can’t we just instead throw it into the category of applied forces to be able to treat the system?
