  The body and spatial representations of rigid body motion correspond,
respectively, to the convective and spatial representations of continuum
dynamics. With a view to developing a unified computational approach for both
types of problems, the discrete Clebsch approach of Cotter and Holm for
continuum mechanics is applied to derive (i) body and spatial representations
of discrete time models of various rigid body motions and (ii) the discrete
momentum maps associated with symmetry reduction for these motions. For these
problems, this paper shows that the discrete Clebsch approach yields a known
class of explicit variational integrators, called discrete Moser-Veselov (DMV)
integrators. The spatial representation of DMV integrators are Poisson with
respect to a Lie-Poisson bracket for the semi-direct product Lie algebra.
Numerical results are presented which confirm the conservative properties and
accuracy of the numerical solutions.
