Dynamics of a Deploying Orbiting Beam-Type Appendage Undergoing Librations

Vibration characteristics associated with a deploying spacecraft appendage in an arbitrary orbit are investigated numerically. In the beginning a rather general formulation of the problem is presented which accounts for the shifting center of mass, appendage offset, arbitrary variation of flexural rigidity along the appendage length, deployment acceleration, satellite librations, etc. The governing nonlinear, nonautonomous, and coupled equations are not amenable to any closed form solution. To gain some appreciation as to the character of the motion, the linearized equations are solved in a quasisteady fashion using the assumed mode procedure over a range of system parameters. Effects of pure flexure, spin, deployment, and orbital motion are isolated and their relative importance established. Although the deployment rate tends to introduce instability, it is the deployment related Coriolis loading which may lead to excessive displacements, particularly if the deployment time is too long. The information should prove particularly useful during the attitude acquisition phase when interactions between the control system, structural flexibility, and vehicle dynamics are particularly significant.