Equations of Motion of Two-Phase Variable Mass Systems With Solid Base

Abstract

This paper develops dynamical equations for variable mass systems that can be viewed, at any given instant, as comprising a solid phase and a fluid phase. The equations of translational and rotational motion are presented, and several versions of each are given. It is shown that some versions have major advantages over others because they involve parameters that are relatively easy to estimate in practical problems, and make close-form solutions possible without the usual penalty of drastic simplifying assumptions. A simple rocket example is presented, and shows that instability cannot be ruled out for such systems. It is shown that system and combustion chamber geometry play a crucial role in the attitude stability of such systems.