The present work aims, primarily, at studying the problem of two bodies with varying mass which has important practical and astrophysical applications. The ejection of mass from any body depends on many parameters, amongst the most important of which are the central condensation (which means, more or less, the degree of rigidity of the body) and the velocity of rotation which provides the external layers with the angular momentum that activates the process of ejection of mass.The procedure followed is developed in the Hamiltonian framework, and is expressed explicitly in terms of the coordinates using Lie series.