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This report presents the results of an investigation of the effects of mass loss on the attitude behavior of spinning bodies in flight. The principal goal is to determine whether there arc circumstances under which the motion of variable mass systems can become unstable in the sense that their transverse angular velocities become unbounded.Obviously, results from a study if this kind would find immediate application in the aerospace field. "The first part of this study feann_s a complete and mathematically rigorous derivation of a set of equations that govern both the translational and rotational motions of general variable mass systems. The remainder of the study is then devoted to the application of the equations obtained to a systematic investigation of the effect of various mass loss scenarios on the dynamics of increasingly complex models of variable mass systems.It is found that mass loss can have a major impact on the dynamics of mechanical systems,includinga possiblechange in the systems stability picture.Factors such as nozzle geometry, combustion chamber geometry, propellant's initial shape, size and relative mass, and propellant location can all have important influences on the system's dynamic behavior. The relative importance of theseparameterson-system motion are quantified in a way thatisusefulfordesignpurposes.ii ACKNOWLEDGMENT

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This paper examines the attitude motion of a cylindrical body with mass loss. It is found that mass variation can have a substantial influence on the behavior of such a system. Specifically, the initial dimensions as well as the manner in which mass loss affects system inertia are found to be key factors in the determination of the characteristics of the lateral motion of the system. In great contrast to the attitude behavior of spinning rigid bodies, oblate variable mass cylinders exhibit divergent transverse attitude motion, while the transverse motion of prolate variable mass cylinders is found to be bounded in general.

This paper studies the attitude dynamics of variable mass systems that have axisymmetric mass distribution and that are subjected to continuous mass variation while in motion. The equations of rotational motion for such systems are solved analytically under the assumption of zero external torque. It is found that such systems can spin up or spin down in free motion, and that the transverse angular velocity magnitude can increase or decrease with time. The analytical conditions for growth or decay of spin rate and lateral angular speed are presented, and these conditions are related to practical design criteria for rocket-type systems.