For n disconnected, non-interacting point particles, the configuration space is R 3 n . In general, however, one is interested in the case where the particles interact: for example, they are specific locations in some assembly of gears, pulleys, rolling balls, etc. often constrained to move without slipping. In this case, the configuration space is not all of R 3 n , but the subspace (submanifold) of allowable positions that the points can take.