might be constrained to move on a specific manifold. For example, if the particle is attached to a rigid linkage, free to swing about the origin, it is effectively constrained to lie on a sphere. Its configuration space is the subset of coordinates in that define points on the sphere . In this case, one says that the manifold is the sphere, i.e. .

For n disconnected, non-interacting point particles, the configuration space is . In general, however, one is interested in the case where the particles interact: