The dynamics of bodies with variable masses

Abstract

The Lie-series provide a convenient and simple method to solve systems of differential equations, especially in problems dealing with variable masses. A system of n-bodies moving isside a cloud and collecting mass is considered. The equations of motion are derived where-by the interchange of momentum is treated as a perturbation. It is shown that the solutions, represented by Lie-series, can be expressed by binomial expansions plus a perturbation which can be solved by interation. In addition, the motion of massless bodies experiencing frictional forces is briefly discussed.