Amit K. Sanyal, Engineering, University of Michigan Dynamics and Control of Extended Bodies in the Presence of Gravity

Abstract. My talk will present some of my research studies on the dynamics and control of extended bodies (like large spacecraft or asteroids) in the presence of a central gravitational field. Such systems have usually been treated in a non-integrated manner until now, where the orbit dynamics is treated as if the body is a mass particle, and the attitude and shape (if the body is flexible) dynamics are based on an extended model. This ignores the essential coupling that is present between these different dynamical degrees of freedom of the system. In particular, for large extended systems, the coupling between the orbital degrees of freedom, and the attitude and shape degrees of freedom, may be utilized to control the orbital motion of the body and change its orbit, as my research shows. This corresponds to transfer of energy from attitude/shape to orbital degrees of freedom. Such control schemes would usually be slow-acting, since most of the energy of the system is in the orbital modes. For numerical simulation of such systems, it is, hence, necessary to have numerical integration algorithms that maintain geometric properties of the system, like conserved quantities, during integration. Symplectic (or variational) integrators, which have often been used for numerical studies of systems in celestial mechanics, are also found to give satisfactory results for these systems. In this talk, I will also describe some symplectic integrators that I have found useful for numerical simulation of such systems. For further information please contact: Matthias Kawski at control@asu.edu