Jacobi dynamics and the N-body problem with variable masses

An appropriate generalization of the Jacobi equation of motion for the pola r moment of inertia I is considered in order to study the N-body problem wi th variable masses. Two coupled ordinary differential equations governing t he evolution of I and the total energy E are obtained. A regularization sch eme for this system of differential equations is provided. We compute some illustrative numerical examples, and discuss an average method for obtainin g approximate analytical solutions to this pair of equations. For a particu lar law of mass loss we also obtain exact analytical solutions. The applica tion of these ideas to other kind of perturbed gravitational N-body systems involving drag forces or a different type of mass variation is also consid ered.