ALGORITHM FOR SIMULATION OF MOTIONS OF VARIABLE-MASS SYSTEMS

Variable-mass systems expel and/or capture particles during motion. A new algorithm for simulation of motions of such systems is introduced. Accordingly, the effect of the expulsion and/or capture of particles on the motion of the system is presented as changes in the integration variables of the governing dynamical equations. In connection with nu merical solutions of the motion equations, the indicated changes are e valuated at each integration step. In contrast, conventional methods d ealing with variable-mass systems give rise to dm/dt v-type terms in the motion equations, terms that account for particle expulsion and/o r capture. The new formulation is developed for simple, nonholonomic s ystems and, with reference to an example, is shown to lead to results satisfying momentum principles. Furthermore, two kinds of systems are identified: continuous-particle-ejecting systems, such as rockets; and discrete-particle-ejecting systems, such as automatic weapons (that f ire rounds, one at a time). In connection with these systems, conditio ns are specified, the satisfaction of which permits the use of the for ce-replacement approach to variable-mass systems on the one hand, and of the new formulation on the other.