MECHANICS OF ROTATING STRUCTURES.

The purpose of this paper is to briefly describe recent research aimed at developing a theory of the rotational dynamics of complex elastic and articulated structures. There are two main sections to this paper. Section 2 presents a derivation of the hybrid system of equations describing the rotational dynamics of a wide class of complex structures. These extend both the classical field equations of solid mechanics and the Euler equations for rotating rigid bodies. Section 3 describes the qualitative dynamical theory of a simple prototype structure consisting of a rigid hub with an elastic appendage undergoing a one degree of freedom rotation. The model includes structural damping, and the focus is on the interplay between energy dissipation and the nonlinear dynamics.