Hamiltonian Structures and Stability for Rigid Bodies with Flexible Attachments.

Abstract

The dynamics of a rigid body with flexible attachments is studied. A general framework for problems of this type is established in the context of Poisson manifolds and reduction. A simple model for a rigid body with an attached linear extensible shear beam is worked out for illustration. Second, the Energy- Casimir method for proving nonlinear stability is recalled and specific stability criteria for our model example are worked out. The Poisson structure and stability results take into account vibrationa of the atring, rotations of the rigid body, their coupling at the point of attachment, and centrifugal and Coriolis forces.