Gyrostat trajectories and core energy

Abstract

Introduction T rigid-body gyrostat dynamic behavior has been rigorously studied in the past in analytical terms' and by qualitative methods. Actual spacecraft of the gyrostat type contain flexible parts, dampers, and fuel slosh, all of which are sources of energy dissipation and that sensibly modify the system's dynamic behavior. The analysis and simulation of dissipative spacecraft is so difficult that workers in this field have often resorted to heuristic methods in order to be able to design such systems. One such method is the so-called energy-sink approach, widely employed for the analysis and design of dual spin spacecraft. Even though the use of this technique in many cases provided the right answers for a successful spacecraft design, it was accompanied by strong disclaimers and even counterexamples, in particular for the case of systems containing driven rotors. The main contention has been that the presence of driven rotors necessarily implies energy sources, contradicting the basic assumption that in the presence of passive dissipation devices the rotational kinetic energy is a decreasing function of time. In Ref. 7 a new hypothesis was advanced, and further studied in Ref. 8, that for a system containing a driven rotor and a dissipative device in the platform, the rotational kinetic energy, less that due to the rotor rotation, relative to the platform itself (a so-called core energy) is effectively a decreasing function of time. The purposes of this work are 1) to perform an analytic-geometric study of the attitude motion of a gyrostat with an asymmetric unbalanced platform and symmetric balanced rotor with a constant rotor/platform relative rate, 2) to establish a relation between the system attitude integral curves and the gyrostat core energy, and 3) to determine the system behavior under energy dissipation.