Geometric mechanics and control of multibody systems

In part I of this dissertation, we extend the field of study of geometric mechanics by explicitly considering the application of geometric mechanics to a class of non-rigid bodies. We introduce double bracket energy sinks which form a very large class of energy dissipation mechanisms for modeling energy dissipation in quasi-rigid bodies. Double bracket energy sinks are derived from double bracket dynamical systems, and energy-Casimir methods are used to prove their energy sink properties. Double bracket energy sinks are shown to be useful for modeling energy dissipation in both axisymmetric and non-axisymmetric quasi-rigid bodies. The importance of quasi-rigid body models in spacecraft dynamics provides the motivation for this study.;In Part II of this dissertation, we apply geometric mechanics to stabilize the intermediate axis rotation of a multibody system in which the configuration manifold Q is not equal to the system symmetry group G. A combination of feedback linearization and momentum feedback are used to produce a closed loop system which is reversible. To our knowledge, we present the first example of the application of nonlinear controls in non-symmetry directions which results in stabilization of intermediate axis rotations. The performance of multiple stable layout somersaults by human gymnasts provides the motivation for this study.