About the Constant of Motion, Lagrangian and Hamiltonian of the Gravitational Attraction of Two Bodies with Variable Mass (Gylden-Meshcherskii problem)

Abstract

The Lagrangian, the Hamiltonian and the constant of motion of the gravitational attraction of two bodies when one of them has variable mass is considered. This is done by choosing the reference system in one of the bodies which allows to reduce the system of equations to 1-D problem. The trajectories found in the space position-velocity,(x,v), are qualitatively different from those on the space position-momentum,(x,p).