Constant of motion, Lagrangian and Hamiltonian of the gravitational attraction of two bodies with variable mass
Abstract
Description
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. The relative and center of mass coordinates are not separated, and choosing the reference system in the body with much higher mass, it is possible to reduce the system of equations to 1-D problem. Then, a constant of motion, the Lagrangian, and the Hamiltonian are obtained. The trajectories found in the space position-velocity,($x,v$), are qualitatively different from those on the space position-momentum,($x,p$).
11 pages, 3 figures, sent to IJMP
11 pages, 3 figures, sent to IJMP