A system of particles in which the interparticle distances rij are fixed and do not change in time. Hence, it retains its shape under the influence of external forces.
Another way to think about a rigid body is a system of particles under a force of constraint that keeps the distances between any pair of particles constant, thereby causing the system to retain its shape overall. This constraint can be thought of as a relation of the sort:
(ri–rj)2 = cij2
for any pair of particles i and j in the rigid body. It satisfies the criterion for holonomic constraint (cij is a constant). As a consequence, the internal potential of a rigid body is constant and the internal forces don’t do any work overall.