  This work presents an elegant formalism to model the evolution of the full
two rigid body problem. The equations of motion, given in a Cartesian
coordinate system, are expressed in terms of spherical harmonics and Wigner
D-matrices. The algorithm benefits from the numerous recurrence relations
satisfied by these functions allowing a fast evaluation of the mutual
potential. Moreover, forces and torques are straightforwardly obtained by
application of ladder operators taken from the angular momentum theory and
commonly used in quantum mechanics. A numerical implementation of this
algorithm is made. Tests show that the present code is significantly faster
than those currently available in literature.
