Given is a set of objects at rest that are in contact with each other, external forces that are applied to them and static friction forces (forces that counteract an applied forces up to a maximum value).
Forces and movement are constrained to one dimension and there is no rotation.
My question would be, after one time step, which objects moved and which objects remained at rest because some static friction forces were too strong?
I am hoping for a general solution without actual physics simulation.
One helpful way to model this problem is with a directed acyclic graph (DAG), with a node for each object and edges between contacting objects.
For tree-like graphs, one can imagine that static forces can only be cancelled out by their "parent" object, however for general DAGs like in the example below, it is unclear to me how static forces should cancel out, because multiple "parents" are possible.
