On the Dynamics of Variable Mass Systems

Abstract

This paper accomplishes two things. It presents a derivation of the equations of motion of variable mass systems. The method presented here is based on Kane's formalism, and is complete, efficient, and mathematically rigorous—avoiding heuristics and many other pitfalls of previous attempts at such derivation. The paper also presents a detailed discussion of the meaning and importance of the various terms of the equations of motion, and the circumstances under which each term can be neglected. It is found that certain judiciously simplified versions of the equations of motion are adequate for most studies. The most important forces contributed by mass variability appear to be the thrust vector and the Coriolis force. The jet damping moment and the moment due to inertia variation are the dominant moments due to mass variability. The study ends with specific equations that are recommended for use in the study of the dynamics of variable mass systems. These equations capture all the important features of the motion of variable mass systems, while remaining simple enough to permit tractable analyses of the behaviour of such systems.