  This paper presents an analytical model and a geometric numerical integrator
for a rigid body connected to an elastic string, acting under a gravitational
potential. Since the point where the string is attached to the rigid body is
displaced from the center of mass of the rigid body, there exist nonlinear
coupling effects between the string deformation and the rigid body dynamics. A
geometric numerical integrator, refereed to as a Lie group variational
integrator, is developed to numerically preserve the Hamiltonian structure of
the presented model and its Lie group configuration manifold. These properties
are illustrated by a numerical simulation.
