Order-n formulation of extrusion of a beam with large bending and rotation

Rosenthal's order-rc algorithm for formulating equations of motion of an /i-degree-of-freedom multibody system is adapted to a situation where n itself changes with time according to a prescribed motion. Effectiveness of modeling a beam in this context by a series of rigid rods connected by rotational springs is demonstrated by comparison to a conventional approach using time-varying shape functions. The formulation is capable of describing large bending deformation of a beam undergoing large overall motion. This is illustrated by three simulations: extrusion/retraction of a beam from/into a base undergoing planar rotation, retraction of a tether into a rotating base, and three-dimensional deformation of a long antenna during spin-up of its base undergoing nonplanar rotation.