respectively, where m i is the mass of FG particle i, M I and I I I I are the mass and inertia tensor, respectively, of CG particle I, U (R N , Ω N ) is the CG potential energy as a function of CG coordinates, and the superscript "T" denotes a matrix transpose. The first and second terms in the sum in Eq. ( ) correspond to the translational and rotational kinetic energies, respectively, of the CG particle. The aims of the coarse-graining procedure are (1) to define a physically appropriate mapping from FG to CG coordinates and (2) to derive expressions for the CG masses, inertia tensors, and potential energy function that best represent the FG system.