Suppose there are a number of objects on top of each other and the bottom one being on top of a frictionless surface. The masses of all of them are given. The coefficients of friction between all surfaces of contact are given. And, the forces acting on each block are given (It's not necessary that there is some force on each object, the force can be zero on some of them and non-zero on others). For simplicity, assume all forces are horizontal and the objects are blocks on top of each other( I've asked a similar question before but it was a homework question). Now, we have to find the motion of each block. The first thing, of which I know, that we do in this kind of problem is to assume that all blocks move with common acceleration. We find the common acceleration and then see if the maximum possible static frictions are exceeded. If they're not then all the blocks move together. But, if frictions are exceeded then the problem becomes very stressful and it's very hard to do the 'guessing' thing. So, is there a systematic mathematical approach to this kind of problem? It would be quite shameful if there still is no such approach given that mathematics has become so advanced.