Analytical Dynamics of Variable-Mass Systems
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Copyright © 2017 by C. Bombardelli. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. The equations of motion for variable-mass systems are commonly assembled in part by adding reactive forces (that is, those terms that are a direct consequence of the mass variation) to other externally applied body and surface forces. A different approach is presented in this study, wherein the contributions from mass variation are naturally created from a proper kinematic development. Specifically, analytical dynamics is used to produce a few equivalent mathematical expressions, each of which is able to generate the governing equations of motion for variable-mass systems: one is similar to the Lagrange equations, another is similar to the Appell equations, and a third represents the Kane equations. The expressions allow one to apply the methods of analytical dynamics toward this class of systems.
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