The use of the constructive method in systems with static friction

The problem of determining the accelerations in a mechanical system with friction at zero initial velocities is discussed. To approximate the solutions, an auxiliary system is constructed in which non-ideal geometrical constraints are produced by elastic forces, the structure of which complies with the static-friction law. It is proved that the auxiliary system is always solvable for the accelerations (possibly, non-uniquely) and hence a solution of the initial system also exists and can be constructed by taking a certain limit.