This paper formulates an optimal control problem for a system of rigid bodies
that are connected by ball joints and immersed in an irrotational and
incompressible fluid. The rigid bodies can translate and rotate in
three-dimensional space, and each joint has three rotational degrees of
freedom. We assume that internal control moments are applied at each joint. We
present a computational procedure for numerically solving this optimal control
problem, based on a geometric numerical integrator referred to as a Lie group
variational integrator.
This paper formulates an optimal control problem for a system of rigid bodies
that are connected by ball joints and immersed in an irrotational and
incompressible fluid. The rigid bodies can translate and rotate in
three-dimensional space, and each joint has three rotational degrees of
freedom. We assume that internal control moments are applied at each joint. We
present a computational procedure for numerically solving this optimal control
problem, based on a geometric numerical integrator referred to as a Lie group
variational integrator.
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.