Dynamics and Stability of Spacecraft with Fluid-Filled Containers

Abstract

In this dissertation, we study the dynamics, stability and control of spacecraft with fluid-filled containers. The spacecraft with fluid-filled containers is modeled as a rigid body containing perfect fluid. A general model for the system is obtained by using a Lagrangian approach where the configuration manifold is the cartesian product of the rotation group and the group of volume preserving diffeomorphisms. The dynamical equations are interpreted as a non-canonical Hamiltonian system on an infinite dimensional Poisson space. The geometry of the model is explicitly given by identifying its Lie-Poisson and Euler-Poincare structure. The equilibria of the system are investigated. Based on the developed model, three control problems are studied for spacecraft with fluid-filled containers. These problems are the stability of rigid rotations equilibria, the stabilization of rigid rotations by means of torque control and the attitude control problem. All stability and control problems are studied in an infinite dimensional nonlinear setting without resorting to approximations. A key feature of this dissertation is the exploitation of the mechanical and geometric structure of the system to address the stability and control problems.