Dynamic interactions and globally optimal maneuver of distributed systems

This dissertation describes the significant interactions between rigid body and flexible-body motions, and the globally optimal maneuver of distributed spacecraft undergoing large overall rigid-body maneuvers and small relative elastic motion. One distinguishes between the rigid-body and flexible-body motions by introducing a tracking coordinate system that coincides with the rigid-body component of the motion and by enforcing the motion relative to the tracking coordinate system (the elastic motion) to be orthogonal to the rigid-body motion. This leads to an infinite set of second-order weakly coupled modal differential equations describing the elastic motion. It is shown that the elastic motion is excited by the rigid body motion through Coriolis terms, angular acceleration terms and centrifugal terms. The Coriolis terms represent a linear time-varying gyroscopic effect, the angular acceleration terms represent a linear time varying circulatory effect and the centrifugal terms represent a linear time-varying stiffness effect. For unidirectional elastic motions, the Coriolis terms and the angular acceleration terms are shown to vanish. For uniform unidirectional elastic motion the centrifugal terms are diagonal and the modal equations become decoupled. Next, the previously indicated intractions are illustrated for spacecraft undergoing bidirectional elastic motions via the dynamics of constantly rotating free-free beams undergoing combined bending and longitudinal vibration. Finally, the dynamics of constantly rotating free-free beams undergoing bending vibration in which the stiffness operator was linerized about the static equilibrium are compared with systems in which the linearization was carried out about the dynamic equilibrium. The comparisons are made for systems rotating about axes perpendicular and parallel to the bending direction.; Using floating coordinates the rigid-body motion and the elastic motion are decoupled thereby allowing the globally optimal maneuver problem to be separated into components associated with the rigid-body and elastic motions. The maneuvers are performed using distributed maneuvering forces based on modal measurements. The modal measurements are extracted from the physical measurements using modal filters. Rest-to-rest maneuvers of a uniform beam illustrate the decentralized nature of the globally optimal solutions.