- #1

etotheipi

For instance, if a ball is rolling down a hill, there exists a normal contact constraint force (satisfying ##N \geqslant 0##) which adjusts its magnitude so that the ball remains on the surface - the constrained motion. But when this force reaches ##N=0##, if the velocity of the ball increases by ##dv## the normal force according to the constrained model would become negative - which evidently can't occur.

So my conclusion was that generally we write the equations of motion for the constrained motion (i.e. at rest, moving in a circle of fixed radius, moving with a platform etc.), and then substitute in the limiting case of a constraint force to solve for the conditions when the motion becomes unconstrained. Is this what is meant when we say something is on the point of e.g. slipping/toppling etc.?

I tried searching for references but the only mentions of constraint forces I could find were in the context of Lagrangian dynamics and other higher level mechanics. I don't know if the usage in that context is similar to what I've said above.