A system of particles in which the interparticle distances r_{ij} 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:

(**r**_{i}–**r**_{j})^{2} = c_{ij}^{2}

for any pair of particles i and j in the rigid body. It satisfies the criterion for holonomic constraint (c_{ij} 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.