A high fidelity model is developed for an elastic string pendulum, one end of
which is attached to a rigid body while the other end is attached to an
inertially fixed reel mechanism which allows the unstretched length of the
string to be dynamically varied. The string is assumed to have distributed mass
and elasticity that permits axial deformations. The rigid body is attached to
the string at an arbitrary point, and the resulting string pendulum system
exhibits nontrivial coupling between the elastic wave propagation in the string
and the rigid body dynamics. Variational methods are used to develop coupled
ordinary and partial differential equations of motion. Computational methods,
referred to as Lie group variational integrators, are then developed, based on
a finite element approximation and the use of variational methods in a
discrete-time setting to obtain discrete-time equations of motion. This
approach preserves the geometry of the configurations, and leads to accurate
and efficient algorithms that have guaranteed accuracy properties that make
them suitable for many dynamic simulations, especially over long simulation
times. Numerical results are presented for typical examples involving a
constant length string, string deployment, and string retrieval. These
demonstrate the complicated dynamics that arise in a string pendulum from the
interaction of the rigid body motion, elastic wave dynamics in the string, and
the disturbances introduced by the reeling mechanism. Such interactions are
dynamically important in many engineering problems, but tend be obscured in
lower fidelity models.