  This paper presents an analytical model and a geometric numerical integrator
for a tethered spacecraft model that is composed of two rigid bodies connected
by an elastic tether. This model includes important dynamic characteristics of
tethered spacecraft in orbit, namely the nonlinear coupling between
deformations of tether, rotational dynamics of rigid bodies, a reeling
mechanism, and orbital dynamics. A geometric numerical integrator, referred 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. The structure-preserving properties are particularly useful for
studying complex dynamics of a tethered spacecraft over a long period of time.
These properties are illustrated by numerical simulations.
